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Steven H.

Calculus 1 / AB

1 month, 3 weeks ago

# Let $f(x) = x^3$. (a) Estimate the values of $f'(0)$, $f'(\frac{1}{2})$, $f'(1)$, $f'(2)$, and $f'(3)$ by using a graphing device to zoom in on the graph of $f$. (b) Use symmetry to deduce the values of $f'(-\frac{1}{2})$, $f'(-1)$, $f'(-2)$, and $f'(-3)$. (c) Use the values from parts (a) and (b) to graph $f'$. (d) Guess a formula for $f'(x)$. (e) Use the definition of derivative to prove that your guess in part (d) is correct.

DM
Oklahoma State University

Let $f(x) = x^3$. (a) Estimate the values of $f'(0)$, $f'(\frac{1}{2})$, $f'(1)$, $f'(2)$, and $f'(3)$ by using a graphing device to zoom in on the graph of $f$. (b) Use symmetry to deduce the values of $f'(-\frac{1}{2})$, $f'(-1)$, $f'(-2)$, and $f'(-3)$. (c) Use the values from parts (a) and (b) to graph $f'$. (d) Guess a formula for $f'(x)$. (e) Use the definition of derivative to prove that your guess in part (d) is correct.

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DM
Oklahoma State University
##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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