a. Explanation Given: Thecurve y = 3 + 4 x 2 − 2 x 3 and the point x = a Concept Used: The slope of the tangent to a curve y = f ( x ) at x = a can be calculated by finding the derivative of the function with respect to x and then substituting x = a Calculation: For the curve y = 3 + 4 x 2 − 2 x 3 The slope is m = d y d x = 0 + b. To determine To find: Theequations of the tangent lines at the points ( 1 , 5 ) and ( 2 , 3 ) c. To determine ToDraw The graph of curve and both the tangent on a common screen.

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3.1, Problem 9E

To determine

To find:The slope of the tangent to the curve y=3+4x2−2x3 at the point where x=a

To determine

To find:Theequations of the tangent lines at the points (1,5) and (2,3)

To determine

ToDraw The graph of curve and both the tangent on a common screen.

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Chapter 3.1, Problem 8E

Chapter 3.1, Problem 10E

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a)Find an equation of the line tangent to the graph of y = x2 + 1 at the point (2, 5)b) Find an equation of the line perpendicular to the graph of y = x2 + 1 at (2, 5)c) Where is the line tangent to the graph of y = x2 + 1 horizontal

1. The slope of the tangent line to the curve y = 2x^3 at the point ( - 5, -250) is: 2. The equation of this tangent line can be written in the form y = mx + b where m is: 3. and where b is:

Find an equation of the tangent line to the parabola y = x2 - 6x + 7 at the point (2, -1). SOLUTION From the previous example, we know the derivative of f(x) = x2 - 6x + 7 at the number a is f '(a) = 2a - 6. Therefore the slope of the tangent line at (2, -1) is f '(2) = 2(2) - 6 = . Thus an equation of the tangent line, shown in the figure, is y - ( ) = (x - )or y = x + 3

Chapter 3 Solutions

Biocalculus

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The slope of the tangent to the curve y = 3 + 4 x 2 − 2 x 3 at the point where x = a

Solution Summary: The author explains how the slope of the tangent to a curve is m=8a-6a2.

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To find:The slope of the tangent to the curve y=3+4x2−2x3 at the point where x=a

To find:Theequations of the tangent lines at the points (1,5) and (2,3)

ToDraw The graph of curve and both the tangent on a common screen.

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Chapter 3 Solutions