Exam 3: Applications of the Derivative

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the $\mathrm{x}$ - axis, symmetry, and asymptotes. Graph each equation. - $y=\frac{4}{5 x-3}$

Using a differential expression, find the change in $V=\frac{4}{3} \pi r^{3}$ from $r=25.00$ in. to 25.10 in.

Use Newton's Method to improve the given estimated solution to at least six significant digits. - $x^{3}-3 x+4=0 ; x=-2$

The town of Darlington plans to build a spherical water tower with an inner diameter of $30.00 \mathrm{~m}$ and sides of thickness $5.00 \mathrm{~cm}$ . Find the approximate volume of steel needed using differentials. If the density of steel is $7800 \mathrm{~kg} / \mathrm{m}^{3}$ , find the approximate amount of steel needed.

In the problems below, determine the intercepts, the intervals in which the curve is above or touching the $\mathrm{x}$ - axis, symmetry, and asymptotes. Graph each equation. - $y=\frac{x}{(x+4)(x-5)}$

Find the inflection point(s) of the function $f(x)=x^{3}-9 x^{2}+15 x+8$ .

Use Newton's Method to improve the given estimated solution to at least six significant digits. - $x+\cos x=0 ; x=-0.5$

A brush fire is burning a circular area whose radius is increasing at a rate of 3 feet per minute. How fast is the area of the fire increasing when its radius is 25 feet?