2. Intro to Derivatives

Find the derivative of the function $f(x)=4x^2-9x$.

Use the definition of a derivative, to find the derivative of the function $g(x)=x^3$ at $x=-1$.

Derivatives using tables Let $h\left(x\right)=f\left(g\right(x\left)\right)$ and $p\left(x\right)=g\left(f\right(x\left)\right)$. Use the table to compute the following derivatives.

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a. $h^{\prime }\left(3\right)$

Derivatives using tables Let $h(x)=f(g(x))$ and $p(x)=g(f(x))$. Use the table to compute the following derivatives.

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b. $h^{\prime }\left(2\right)$

Derivatives using tables Let $h(x)=f(g(x))$ and $p(x)=g(f(x))$. Use the table to compute the following derivatives.

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c. $p^{\prime }\left(4\right)$

Derivatives using tables Let $h(x)=f(g(x))$ and $p(x)=g(f(x))$. Use the table to compute the following derivatives.

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d. $p^{\prime }\left(2\right)$

For the function $f\left(x\right)=3x^2$, what is the multiplicative rate of change of the function, that is, what is its derivative as a function of $x$?

Suppose the graph of the function $f\left(x\right)$ passes through the points $(2,3)$ and $(4,7)$. What is the average rate of change of $f\left(x\right)$ between $x=2$ and $x=4$? Round your answer to the nearest tenth.