91Ó°ÊÓ

Differentiate each function $$ y=(3-2 x)^{2} $$ Check by expanding and then differentiating.

Find \(d^{2} y / d x^{2}\) $$ y=x^{4}-7 $$

(a) find the simplified form of the difference quotient and then (b) complete the following table. $$ \begin{array}{|c|l|l|} \hline x & h & \frac{f(x+h)-f(x)}{h} \\ \hline 5 & 2 & \\ \hline 5 & 1 & \\ \hline 5 & 0.1 & \\ \hline 5 & 0.01 & \\ \hline \end{array} $$ $$ f(x)=5 x^{2} $$

a) Graph the function. b) Draw tangent lines to the graph at points whose \(x\) -coordinates are \(-2,0,\) and 1 c) Find \(f^{\prime}(x)\) by determining \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\). d) Find \(f^{\prime}(-2), f^{\prime}(0),\) and \(f^{\prime}(1) .\) These slopes should match those of the lines you drew in part (b). $$f(x)=\frac{1}{2} x^{2}$$

Differentiate two ways: first, by using the Product Rule; then, by multiplying the expressions before differentiating. Compare your results as a check. Use a graphing calculator to check your results. \(y=x^{9} \cdot x^{4}\)

Complete each of the following statements. As x approaches______________ , the value of -3x approaches 6.

Find \(\frac{d y}{d x}\) $$ y=x^{8} $$

Find \(d^{2} y / d x^{2}\) $$ y=x^{5}+9 $$

a) Graph the function. b) Draw tangent lines to the graph at points whose \(x\) -coordinates are \(-2,0,\) and 1 c) Find \(f^{\prime}(x)\) by determining \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\). d) Find \(f^{\prime}(-2), f^{\prime}(0),\) and \(f^{\prime}(1) .\) These slopes should match those of the lines you drew in part (b). $$f(x)=\frac{3}{2} x^{2}$$

Find \(\frac{d y}{d x}\). $$ y=x^{7} $$