The goal of this problem is to compute the value of the derivative at a point for several different functions, where for each one we do so in three different ways, and then to compare the results to see that each produces the same value. For each of the following functions, use the limit definition of the derivative to compute the value of f'(a) using three different approaches: strive to use the algebraic approach first (to compute the limit exactly), then test your result using numerical evidence (with small values of h), and finally plot the graph of y = f(x) near (a, f(a)) visually. Compare your findings among all three approaches; if you are unable to complete the algebraic approach, still work numerically and graphically. Note: At least one graph will have a derivative that does not exist so please enter DNE ƒ(x) = x² − 6x, a = 4 f(x) f(x) = f(x) = 1 = x " a = - 4 Note: the lim sin(x), a = π 2 sin (h) h h→0 √x, a = 1 Hint = 1 and the lim 1 h→0 f(x) = 7 x − 4|, a = 4 cos(h) h = 0

The goal of this problem is to compute the value of the derivative at a point for several different functions, where for each one we do so in three different ways, and then to compare the results to see that each produces the same value. For each of the following functions, use the limit definition of the derivative to compute the value of f'(a) using three different approaches: strive to use the algebraic approach first (to compute the limit exactly), then test your result using numerical evidence (with small values of h), and finally plot the graph of y = f(x) near (a, f(a)) visually. Compare your findings among all three approaches; if you are unable to complete the algebraic approach, still work numerically and graphically. Note: At least one graph will have a derivative that does not exist so please enter DNE ƒ(x) = x² − 6x, a = 4 f(x) f(x) = f(x) = 1 = x " a = - 4 Note: the lim sin(x), a = π 2 sin (h) h h→0 √x, a = 1 Hint = 1 and the lim 1 h→0 f(x) = 7 x − 4|, a = 4 cos(h) h = 0

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.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 1CR

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