Explanation:step one: find the derivative of the equation. Step two: Since a horizontal line has a slope of 0, set the derivative to equal 0 and solve. Step three: plug the x-values found in step 2 back into the original equation to get the y-coordinates of the points on the curve.
#y(-2)= 21# Step four: write out the coordinates of the points with a slope of zero. Consider the following line. graph{y = 0x + 1 [-10, 10, -5, 5]} What can we say about this line? We can say that it is horizontal. Let's look at the slope. #m = (y_2 - y_1)/(x_2 - x_1) = (1 - 1)/(0 - 5) = 0/-5 = 0# The slope is #0#. So, the slope of any horizontal line is #0#, since any other horizontal line will be parallel to this one. Hence, we need to find the points on the derivative where the slope of the tangent is #0#. The derivative can be found using a combination of the sum/difference and power rules. #y' = 6x^2 + 6x - 12# The slope of the tangent is given by plugging in a point, #x = a#, into the derivative. Hence, we can set #y'#, the slope, to #0# and solve for #x#. #0 = 6x^2 + 6x - 12# #0 = 6(x^2 + x - 2)# #0 = (x + 2)(x - 1)# #x = -2 and 1# All that is left to do is determine the corresponding y-coordinates that the function passes through. #y = 2(-2)^3 + 3(-2)^2 - 12(-2) + 1 = 2(-8) + 3(4) + 24 + 1 = 21# AND #y = 2(1)^3 + 3(1)^2 - 12(1) + 1 = 2 + 3 - 12 + 1 = -6# Hence, the points where the tangent is horizontal are #(-2, 21)# and #(1, -6)#. Hopefully this helps! 2.3 pt 2 14  Transcribed Image Text:Find the points on the curve y = 2x3 + 3x2 - 12x + 8 where the tangent line is horizontal. (х, у) (smaller x-value) (х, у) (larger x-value) Need Help? Watch It Read It Q: (a) Find an equation of the tangent line to the curve y = 16x sin(x) at the point (7/2, 87). A: Click to see the answer Q: What is the value of the slope of the tangent line to the curve x2- 2xy – 2y²=1 passing through the… A: In this question , we can find the value of the slope of the given curve . Differentiate the given… Q: the Curve y=2x=3== r x + 20 where the tangent is parallel to the X-aXis Find the points on 12 X + 20 A: When the tangent is parallel to the x-axis, dy/dx will be equal to 0 Q: Draw a diagram to show that there are two tangent lines to the parabola of y = x2 that pass through… A: Click to see the answer Q: Consider the curve parameterized by x 3t2 3 and y 2t°. Find equations for all tangent lines to this… A: Here we have to find the equation of tangent line. Q: Find the equation of the tangent line to the curve y=9√x at the point (4,18). The equation of the… A: Find y' and the value of y' is the slope for y.Find the slope m at (4,18). Q: 8.) What is the slope of a tangent line tangent to curve g(x) = v5x -8 at point x= 37 a.) 7 b)V7 d.)… A: Since you have asked multiple questions, we will solve the first question (i.e., Question-8) for… Q: S ize Find an equation of the line tangent to the curve defined by x + 5xy + y² = 7 at the point (1,… A: Click to see the answer Q: NO. DATE L Find the equation of the line tangert to the curve 4= x? coxo+ Ex +2 - at its point of… A: Click to see the answer Q: What is the value of the slope of the tangent line to the curve 2+4.xy + y² = 13 passing through the… A: Click to see the answer Q: Consider the curve parameterized by a 3t2 15 and y= 2t3 15. Find equations for all tangent lines to… A: We have to find the tangent to the parametric curve. Q: Find an equation of the tangent line to the curve y = at the point (1,). 8 + Vx Confirm this tangent… A: Click to see the answer Q: Find the equation of the tangent line to the curve y=8ln(x3 −63) at the point (4,0) A: Click to see the answer Q: The curve y = ax2 + b and y = 2x2+cx have a common tangent line at the point (-1,0). Find a+b+c at… A: To find: value of a + b + c Q: Find the point on the curve y=v2z+2 which is closest to the point (4, 0) Submit Question A: To obtain closest point on the given curve from the pont (4,0) Firstly we construct a graph of the… Q: Find the points on the curve y = 2x3 + 3x2 − 12x + 5 where the tangent line is horizontal. (x,… A: Click to see the answer Q: Find the equation of the tangent line to the curve y = 4sin z at the point The equation of this… A: To find the equation of the tangent line to the curve y=4sinx at the point π6,2. Solution: Firstly,… Q: Find an equation of the tangent plane to the surface at the given point. 3 x2 + 3z?ev - x = 52, P =… A: Click to see the answer Q: Find the point at which the line y = 8x – 31 is tangent to the graph of y = eXf-16). %3D The point… A: Click to see the answer Q: How many tangent lines to the curve y= x /(x+1) passthrough the point ( 1,2) ? At which points do… A: Given : y=xx+1 pass through the point (1, 2) To find: The number of tangent lines to the curve y =… Q: What is the value of the slope of the tangent line to the curve x2- 2xy – 2y²=1 passing through the… A: Click to see the answer Q: Find the point (x0,y0) on the graph y=x^3 + 6x^2 +3x -5 at which the slope of the tangent line has… A: Click to see the answer Q: Determine the point on the curve y 16 a² where the tangent line is horizontal. A (2, 12) (-2, -12)… A: Click to see the answer Q: Consider the curve y= x^2 +2x +5 (a) Find the slope of the secant line to curve through the points… A: Click to see the answer Q: What is the slope of the tangent line to the graph of y= x*-3x2 + x +2 at x-17 [a) What is the… A: Click to see the answer Q: Determine whether the statement is true or false. An equation of the tangent line to the parabola y… A: Click to see the answer Q: Find the equations of the tangent lines at the point where the curve crosses itself. x = 3 - 6t y =… A: The given curve is: x=t3-6ty=t2 Q: nd the point (both x and y coordinates) where the tangen A: Click to see the answer Q: The curve y = f(x) has a y – intercept of 3. The tangent to this curve at the point (x, y) has an x… A: Given that the curve y=f(x) has a y-intercept of 3. That means y(0)=3. also given that the tangent… Q: Find an equation of the tangent plane to the surface at the given point. x² + y? - 5z2 = 69, (-7,… A: Click to see the answer Q: 3t2 + 1, y = 2t3 +1 that pass through the point Find equations of the tangents to the curve x = (4,… A: NOTE: Refresh your page if you can't see any equations. . the given point is (4,3) sot ake y=3 Q: Consider the curve parameterized by x = 3t²3 and y = 2t³. Find equations for all tangent lines to… A: Click to see the answer Q: What is the value of the slope of the tangent line to the curve x2- 2xy – 2y² = 1 passing through… A: Click to see the answer Q: Find the equation of the line tangent to the curve y = Vx at the point (4,2). Hint: Write vx = x1/2… A: Given: y=x at the point (4, 2) To find: The equation of tangent to the curve y=x at the point (4,… Q: Find an equation of the tangent line to the curve at the given point. x + 1 (6, -7) x - 7 y =y= -8x… A: y= x+1 / x-7 (6,-7 ) x- y - =13 Q: Find an equation of the tangent line to the curve 2(x² + y)² = 25(x² – y²) (a lemniscate) at the… A: Given that 2x2+y22=25x2-y2To find : equation of tangent line at point 3,1Solution… Q: At a particular point of the curve y = 2x2 -x+q, the equation of the tangent is y = 3x-5. [7 marks]… A: Click to see the answer Q: a. Determine the points where the curve 4x + 2y -y =1 has a vertical tangent line. b. Does the curve… A: Consider the given curve 4x + 2y2 – y = 1 Q: What is the value of the slope of the tangent line to the curve x2+4xy+y²=13 passing through the… A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative… Q: cosx Find the equation of the tangent to the curve y=- at x= 2x 2 A: Click to see the answer Knowledge Booster Recommended textbooks for you Calculus: Early Transcendentals ISBN:9781285741550 Author:James Stewart Publisher:Cengage Learning Thomas' Calculus (14th Edition) ISBN:9780134438986 Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir Publisher:PEARSON Calculus: Early Transcendentals (3rd Edition) ISBN:9780134763644 Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz Publisher:PEARSON Calculus: Early Transcendentals ISBN:9781319050740 Author:Jon Rogawski, Colin Adams, Robert Franzosa Publisher:W. H. Freeman Precalculus ISBN:9780135189405 Author:Michael Sullivan Publisher:PEARSON Calculus: Early Transcendental Functions ISBN:9781337552516 Author:Ron Larson, Bruce H. Edwards Publisher:Cengage Learning Calculus: Early Transcendentals ISBN:9781285741550 Author:James Stewart Publisher:Cengage Learning Thomas' Calculus (14th Edition) ISBN:9780134438986 Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir Publisher:PEARSON Calculus: Early Transcendentals (3rd Edition) ISBN:9780134763644 Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz Publisher:PEARSON Calculus: Early Transcendentals ISBN:9781319050740 Author:Jon Rogawski, Colin Adams, Robert Franzosa Publisher:W. H. Freeman Precalculus ISBN:9780135189405 Author:Michael Sullivan Publisher:PEARSON Calculus: Early Transcendental Functions ISBN:9781337552516 Author:Ron Larson, Bruce H. Edwards Publisher:Cengage Learning |
At what point along the curve y 3x2 12x 8 is the slope of the tangent line horizontal?
Postagens relacionadas
direito autoral © 2024 cemle Inc.
