91Ó°ÊÓ

For the following exercises, assume that \(f(x)\) and \(g(x)\) are both differentiable functions with values as given in the following table. Use the following table to calculate the following derivatives. $$\begin{array}{|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} \\ \hline f(x) & {3} & {5} & {-2} & {0} \\ \hline g(x) & {2} & {3} & {-4} & {6} \\ \hline f^{\prime}(x) & {-1} & {7} & {8} & {-3} \\ \hline g^{\prime}(x) & {4} & {1} & {2} & {9} \\ \hline\end{array}$$ Find \(h^{\prime}(1)\) if \(h(x)=x f(x)+4 g(x)\)

For the following exercises, assume that \(f(x)\) and \(g(x)\) are both differentiable functions with values as given in the following table. Use the following table to calculate the following derivatives. $$\begin{array}{|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} \\ \hline f(x) & {3} & {5} & {-2} & {0} \\ \hline g(x) & {2} & {3} & {-4} & {6} \\ \hline f^{\prime}(x) & {-1} & {7} & {8} & {-3} \\ \hline g^{\prime}(x) & {4} & {1} & {2} & {9} \\ \hline\end{array}$$ Find \(h^{\prime}(2)\) if \(h(x)=\frac{f(x)}{g(x)}\)

Assume that \(f(x)\) and \(g(x)\) are both differentiable functions with values as given in the following table. Use the following table to calculate the following derivatives. $$ \begin{array}{|c|c|c|c|c|} \hline \boldsymbol{x} & 1 & 2 & 3 & 4 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & 3 & 5 & -2 & 0 \\ \hline \boldsymbol{g}(\boldsymbol{x}) & 2 & 3 & -4 & 6 \\ \hline \boldsymbol{f}^{\prime}(\boldsymbol{x}) & -1 & 7 & 8 & -3 \\ \hline \boldsymbol{g}^{\prime}(\boldsymbol{x}) & 4 & 1 & 2 & 9 \\ \hline \end{array} $$ Find \(h^{\prime}(2)\) if \(h(x)=\frac{f(x)}{g(x)}\).

For the following exercises, assume that \(f(x)\) and \(g(x)\) are both differentiable functions with values as given in the following table. Use the following table to calculate the following derivatives. $$\begin{array}{|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} \\ \hline f(x) & {3} & {5} & {-2} & {0} \\ \hline g(x) & {2} & {3} & {-4} & {6} \\ \hline f^{\prime}(x) & {-1} & {7} & {8} & {-3} \\ \hline g^{\prime}(x) & {4} & {1} & {2} & {9} \\ \hline\end{array}$$ Find \(h^{\prime}(3)\) if \(h(x)=2 x+f(x) g(x)\).

Assume that \(f(x)\) and \(g(x)\) are both differentiable functions with values as given in the following table. Use the following table to calculate the following derivatives. $$ \begin{array}{|c|c|c|c|c|} \hline \boldsymbol{x} & 1 & 2 & 3 & 4 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & 3 & 5 & -2 & 0 \\ \hline \boldsymbol{g}(\boldsymbol{x}) & 2 & 3 & -4 & 6 \\ \hline \boldsymbol{f}^{\prime}(\boldsymbol{x}) & -1 & 7 & 8 & -3 \\ \hline \boldsymbol{g}^{\prime}(\boldsymbol{x}) & 4 & 1 & 2 & 9 \\ \hline \end{array} $$ Find \(h^{\prime}\) (3) if \(h(x)=2 x+f(x) g(x)\).

For the following exercises, assume that \(f(x)\) and \(g(x)\) are both differentiable functions with values as given in the following table. Use the following table to calculate the following derivatives. $$\begin{array}{|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} \\ \hline f(x) & {3} & {5} & {-2} & {0} \\ \hline g(x) & {2} & {3} & {-4} & {6} \\ \hline f^{\prime}(x) & {-1} & {7} & {8} & {-3} \\ \hline g^{\prime}(x) & {4} & {1} & {2} & {9} \\ \hline\end{array}$$ Find \(h^{\prime}(4)\) if \(h(x)=\frac{1}{x}+\frac{g(x)}{f(x)}\).

Assume that \(f(x)\) and \(g(x)\) are both differentiable functions with values as given in the following table. Use the following table to calculate the following derivatives. $$ \begin{array}{|c|c|c|c|c|} \hline \boldsymbol{x} & 1 & 2 & 3 & 4 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & 3 & 5 & -2 & 0 \\ \hline \boldsymbol{g}(\boldsymbol{x}) & 2 & 3 & -4 & 6 \\ \hline \boldsymbol{f}^{\prime}(\boldsymbol{x}) & -1 & 7 & 8 & -3 \\ \hline \boldsymbol{g}^{\prime}(\boldsymbol{x}) & 4 & 1 & 2 & 9 \\ \hline \end{array} $$ Find \(h^{\prime}(4)\) if \(h(x)=\frac{1}{x}+\frac{g(x)}{f(x)}\).

For the following exercises, a. evaluate \(f^{\prime}(a),\) and b. graph the function \(f(x)\) and the tangent line at \(x=a\) $$\mathrm{[T]} f(x)=2 x^{3}+3 x-x^{2}, a=2$$

For the following exercise, a. evaluate \(f^{\prime}(a),\) and b. graph the function \(f(x)\) and the tangent line at \(x=a\). $$ f(x)=2 x^{3}+3 x-x^{2}, a=2 $$

For the following exercise, a. evaluate \(f^{\prime}(a),\) and b. graph the function \(f(x)\) and the tangent line at \(x=a\). $$ f(x)=\frac{1}{x}-x^{2}, a=1 $$