CPM Homework Help : APCALC Problem 3-150

Use the definition of a derivative to write an equation for $y^\prime$ if $y = \frac { 3 } { 4 }x^2 − 11x + 34$ . Confirm your answer with the Power Rule.

Hint:

Hana's Definition of derivative:

$f'(x)=\lim\limits_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

Step 1:

Substitute:

$f'(x)=\lim\limits_{h\rightarrow 0}\frac{\left (\frac{3}{4}(x+h)^{2}-11(x+h)+32 \right )-\left ( \frac{3}{4}x^{2}-11x+32 \right )}{h}$

Step 2:

Expand the numerator and combine like terms.

Step 3:

Factor an $h$ out of the numerator so you can 'cancel out' the $h$ in the denominator.

Step 4:

Evaluate the limit. You should get the same derivative you found with the Power Rule.