Mathematics

Problem

49. Let

f(x)=2 x^{2}+3 x+1

and

g(x)=x^{3}+1

. (a) Compute the derivative of

f

. (b) Compute the derivative of

g

. (c) Using

x=2

and

h=0.001

, compute the standard difference quotient

\frac{f(x+h)-f(x)}{h}

and the symmetric difference quotient

\frac{f(x+h)-f(x-h)}{2 h} .

(d) Using

x=2

and

h=0.001

, compare the approximations to

f^{\prime}(2)

in part (c). Which is the better approximation? (e) Repeat parts (c) and (d) for

g