Consider the function f: [0, 3] → R defined by f(x) = sin(2x). A. Does the Mean Value Theorem apply to function f? Explain. B. In slope-intercept form, find the equation of the secant line through the points (0, f(0)) and (3, ƒ (³)). C. Find a point c on the interval (0, ³) that satisfies the Mean Value Theorem. (For this part, you will need to use a calculator or a trig table.) D. In slope-intercept form, find the equation of the tangent line to function f at point c. How does the slope of this line compare to the slope of the secant line from Part B?

Consider the function f: [0, 3] → R defined by f(x) = sin(2x). A. Does the Mean Value Theorem apply to function f? Explain. B. In slope-intercept form, find the equation of the secant line through the points (0, f(0)) and (3, ƒ (³)). C. Find a point c on the interval (0, ³) that satisfies the Mean Value Theorem. (For this part, you will need to use a calculator or a trig table.) D. In slope-intercept form, find the equation of the tangent line to function f at point c. How does the slope of this line compare to the slope of the secant line from Part B?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.4: Definition Of The Derivative

Problem 1YT: YOUR TURN For the graph of f(x)=x2x, a find the equation of the secant line through the points where...

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