91Ó°ÊÓ

Find functions \(f\) and \(g\) such that the given function is the composition \(f(g(x))\). $$\sqrt{x^{2}-9}+5$$

Find the average rate of change of the given function between the following pairs of \(x\) -values. [Hint: See page 94.] a. \(x=1\) and \(x=3\) b. \(x=1\) and \(x=2\) c. \(x=1\) and \(x=1.5\) d. \(x=1\) and \(x=1.1\) e. \(x=1\) and \(x=1.01\) f. What number do your answers seem to be approaching? $$f(x)=x^{2}+x$$

Find the derivative of each function. $$g(w)=6 \sqrt[3]{w}$$

Find each limit by graphing the function and using TRACE or TABLE to examine the graph near the indicated \(x\) -value. $$\lim _{x \rightarrow 1} \frac{\frac{1}{x}-1}{1-x}$$

Find the derivative of each function by using the Product Rule. Simplify your answers. $$f(x)=6 \sqrt[3]{x}(2 x+1)$$

Find the average rate of change of the given function between the following pairs of \(x\) -values. [Hint: See page 94.] a. \(x=1\) and \(x=3\) b. \(x=1\) and \(x=2\) c. \(x=1\) and \(x=1.5\) d. \(x=1\) and \(x=1.1\) e. \(x=1\) and \(x=1.01\) f. What number do your answers seem to be approaching? $f(x)=2 x^{2}+5$$

Find functions \(f\) and \(g\) such that the given function is the composition \(f(g(x))\). $$\sqrt[3]{x^{3}+8}-5$$

For each function, find a. \(f^{\prime \prime}(x)\) and b. \(f^{\prime \prime}(3)\). $$f(x)=\frac{x-2}{4 x}$$

Find the derivative of each function. $$g(w)=12 \sqrt{w}$$

Find each limit by graphing the function and using TRACE or TABLE to examine the graph near the indicated \(x\) -value. $$\lim _{x \rightarrow 1.5} \frac{2 x^{2}-4.5}{x-1.5}$$