Use a graphing calculator or a CAS to plot the graph of each of the following functions on [-1,7]. Determine the coordinates of any global extrema and any inflection points. You should be able to give answers that are accurate to at least one decimal place. (a) $f(x)=x \sqrt{x^2-6 x+40}$ (b) $f(x)=\sqrt{|x|}\left(x^2-6 x+40\right)$ (c) $f(x)=\sqrt{x^2-6 x+40} /(x-2)$ (d) $f(x)=\sin \left[\left(x^2-6 x+40\right) / 6\right]$

Let f be a continuous function with $f(0)=f(2)=0$. If the graph of $y=f^{\prime}(x)$ is as shown in Figure 14, sketch a possible graph for y=f(x).

In given problem, evaluate the indicated integrals.

$$\int z\left(2 z^2-3\right)^{1 / 3} d z$$

Sketch the graph of P(n) of given problem, and from it estimate the value of n that maximizes P. Find this n exactly by the methods of calculus.

A 20-gallon barrel, as shown in given figure, leaks at the constant rate of 0.1 gallon per day. Sketch a plot of the height h of the water as a function of time t, assuming that the barrel is full at time t=0. In your graph, pay special attention to the concavity of h.

Use the information in given problem to write an expression for the total monthly profit $P(n), n \geq 100$.

In given problem, evaluate the indicated integrals.

$$\int y \sqrt{y^2-4} d y$$

Repeat previous problem for given figure.

Let f be a continuous function and let $f^{\prime}$ have the graph shown in given figure. Sketch a possible graph for f and answer the following questions.

(a) Where is f increasing? Decreasing?

(b) Where is f concave up? Concave down?

(c) Where does f attain a local maximum? A local minimum?

(d) Where are there inflection points for f?

In given problem, evaluate the indicated integrals.

$$\int \frac{y^3-9 y \sin y+26 y^{-1}}{y} d y$$

A liquid is poured into the container shown in given figure at the rate of 3 cubic inches per second. The container holds about 24 cubic inches. Sketch a graph of the height h of the liquid as a function of time t. In your graph, pay special attention to the concavity of h.

The manufacturer of Zbars estimates that 100 units per month can be sold if the unit price is $250 and that sales will increase by 10 units for each$5 decrease in price. Write an expression for the price p(n) and the revenue R(n) if n units are sold in one month, $n \geq 100$

The fixed monthly cost of operating a plant that makes Zbars is $7000, while the cost of manufacturing each unit is$100. Write an expression for C(x), the total cost of making x Zbars in a month.

Let $F_0(x)=x \sin x$ and $F_{n+1}(x)=\int F_n(x) d x$.

(a) Determine $F_1(x), F_2(x), F_3(x)$, and $F_4(x)$.

(b) On the basis of part (a), conjecture the form of $F_{16}(x)$