Evaluate the difference quotient for the function. $$f ( x ) = 4 x ^ { 2 } - 14$$
A) $ \quad 1 $
B) $ \quad 8 $
C) $ \quad 4 x+h $
D) $ 8 x+4 h $
E) 4

Question

Quizplus · Accepted Answer

The difference quotient for a function is given by 
$$ \frac { f ( x + h ) - f ( x ) } { h } $$
Substitute the given function into this expression and simplify:
$$ \frac { f ( x + h ) - f ( x ) } { h } = \frac { 4 ( x + h ) ^ { 2 } - 14 - ( 4 x ^ { 2 } - 14 ) } { h } $$
$$ = \frac { 4 ( x ^ { 2 } + 2 x h + h ^ { 2 } ) - 4 x ^ { 2 } } { h } = \frac { 8 x h + 4 h ^ { 2 } } { h } = 8 x + 4 h $$
Therefore, the correct choice is D.

Evaluate the Difference Quotient for the Function f(x)=4x2−14f ( x ) = 4 x ^ { 2 } - 14f(x)=4x2−14

Evaluate the Difference Quotient for the Function $f ( x ) = 4 x ^ { 2 } - 14$