   Chapter 2.R, Problem 52E

Chapter
Section
Textbook Problem

# (a) If f ( x ) = 4 x − tan x , − π / 2 < x < π / 2 , find f ' and f " .(b) Check to see that your answer to part (a) is reasonable by comparing the graphs of f , f ' , and f "

To determine

(a)

To find:f'and f".

Explanation

1) Formula:

i. difference rule:

ddxfx-gx=ddxfx-ddxg(x)

ii. Power rule combined with chain rule:

ddxf(x)n=nfxn-1.f'(x)

iii. constant function rule:

ddxc=0 where c is constant.

iv.Equation of tangent line to the curve y=f(x) at point (a,f(a)) is,

(y-f(a))=f(a)(x-a)

3) Given:

y=fx=4x-tanx , -π2<c<π2

4) Calculation:

Differentiate given equation with respect to x,

f'x=ddx[4x-tanx]

Using product rule,

ddx

To determine

(b)

To check: answer to part(a) is reasonable by comparing  graphs of f,f,f

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