91Ó°ÊÓ

Differentiate each function. $$f(t)=\frac{t}{5+2 t}-2 t^{4}$$

Differentiate each function. $$G(x)=\sqrt[3]{x^{5}+6 x}$$

Based on data from Major League Baseball, the average price of a ticket to a major league game can be approximated by \(p(x)=0.03 x^{2}+0.56 x+8.63\) where \(x\) is the number of years after 1991 and \(p(x)\) is in dollars. (Source: Based on data from www.teammarketing.com.) a) Find \(p(4).\) b) Find \(p(17).\) c) Find \(p(17)-p(4).\) d) Find \(\frac{p(17)-p(4)}{17-4},\) and interpret this result.

Draw a graph that is continuous, but not differentiable, at \(x=3.\)

The initial substitution of \(x=a\) yields the form \(0 / 0 .\) Look for ways to simplify the function algebraically, or use a table and/or a graph to determine the limit. When necessary, state that the limit does not exist. $$\lim _{x \rightarrow-1} \frac{x^{2}+5 x+4}{x^{2}+2 x+1}$$

Find each derivative. $$\frac{d}{d x}(-2 \sqrt[3]{x^{5}})$$

Differentiate each function. $$\begin{aligned} &F(x)=(x+3)^{2}\\\ &\text { [Hint: }(x+3)^{2}=(x+3)(x+3) \cdot 1 \end{aligned}$$

Find \(y^{\prime \prime}\). $$y=2 x^{5 / 4}+x^{1 / 2}$$

The initial substitution of \(x=a\) yields the form \(0 / 0 .\) Look for ways to simplify the function algebraically, or use a table and/or a graph to determine the limit. When necessary, state that the limit does not exist. $$\lim _{x \rightarrow 2} \frac{x^{2}+3 x-10}{x^{2}-4 x+4}$$

Find \(y^{\prime \prime}\). $$y=3 x^{4 / 3}-x^{1 / 2}$$