CPM Homework Help : CALC Problem 3-92

While using the definition of a derivative, Lulu used the following limit. For what function was she finding the derivative? How can you tell? Without simplifying this expression, determine the limit.

$\lim\limits_ { h \rightarrow 0 } \frac { ( 6 ( x + h ) ^ { 2 } - 5 ( x + h ) + 3 ) - ( 6 x ^ { 2 } - 5 x + 3 ) } { h }$

Step 1:

Lulu used Hana's definition of the derivative;
$f'(x)=\lim\limits_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$
Examine Lulu's limit: What if $f(x)$ ?

Step 2:

Once you determine $f(x)$ , use the Power Rule to find $f^\prime(x)$ , the derivate function.This derivative function is the value of Lulu's limit as $h→0$ .