💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

DM

# 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.

## a) $f^{\prime}(0)=0 ; f^{\prime}(1 / 2)=.7 ; f^{\prime}(1)=3 ; f^{\prime}(2)=10 ; f^{\prime}(3)=25$b) $f^{\prime}(0)=0 ; f^{\prime}(-1 / 2)=0.7 ; f^{\prime}(-1)=3 ; f^{\prime}(-2)=10 ; f^{\prime}(-3)=25$c) (Graph uanvailable)d) $f^{\prime}(x)=a x^{2} ; a>0$e) $f^{\prime}(x)=3 x^{2}$

Limits

Derivatives

### Discussion

You must be signed in to discuss.
##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp

### Video Transcript

DM
Oklahoma State University

Limits

Derivatives

Lectures

Join Bootcamp