Chapter 3.4, Problem 48E

To determine

a.

The value of $f^{\prime }\left(3\right)$ and also find the approximation using the formula $\frac{f\left(x+h\right)-f\left(x\right)}{h}$ and $\frac{f\left(x+h\right)-f\left(x-h\right)}{2h}$ for $h=0.1$.

To determine

b.

The value of $f^{\prime }\left(3\right)$ and also find the approximation using the formula $\frac{f\left(x+h\right)-f\left(x\right)}{h}$ and $\frac{f\left(x+h\right)-f\left(x-h\right)}{2h}$ for $h=0.01$.

To determine

c.

The value of $f^{\prime }\left(3\right)$ and also find the approximation using the formula $\frac{f\left(x+h\right)-f\left(x\right)}{h}$ and $\frac{f\left(x+h\right)-f\left(x-h\right)}{2h}$ for $h=0.1$.

To determine

d.

The value of $f^{\prime }\left(3\right)$ and also find the approximation using formula $\frac{f\left(x+h\right)-f\left(x\right)}{h}$ and $\frac{f\left(x+h\right)-f\left(x-h\right)}{2h}$ for $h=0.01$.

To determine

e.

The value of $f^{\prime }\left(3\right)$ and also find the approximation using formula $\frac{f\left(x+h\right)-f\left(x\right)}{h}$ and $\frac{f\left(x+h\right)-f\left(x-h\right)}{2h}$ for $h=0.1$.

To determine

f.

The value of $f^{\prime }\left(3\right)$ and also find the approximation using formula $\frac{f\left(x+h\right)-f\left(x\right)}{h}$ and $\frac{f\left(x+h\right)-f\left(x-h\right)}{2h}$ for $h=0.01$.

To determine

g.

Which approximation formula gives better approximation?