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Chapter 2: Q. 42 (page 166)

For each function f and value x = c in Exercises 35鈥�44, use a sequence of approximations to estimate f'(c). Illustrate your work with an appropriate sequence of graphs of secant lines.

f(x)=arctan鈦�x,c=0

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01

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f(x)=arctan鈦�x,c=0

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Most popular questions from this chapter

For each function fgraphed in Exercises 65-68, determine the values of xat which ffails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=x-12(x2-1)3

Find the derivative of the absolute value function and piecewise defined function

f(x)=3x+1ifx鈮�1x3ifx>1

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c) for each function f and value x=c in Exercises 23鈥�38.

24.f(x)=x3,x=1

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c)for each function f and value x=c in Exercises 23鈥�38.

27.f(x)=1-x3,x=-1
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