Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x ) = x 2 $-$ 5 x + 2.
A) 2 a + h
B) 2 a + h $-$ 5
C) $-$ 2 a $-$ h + 5
D) a + h $-$ 2

Question

Quizplus · Accepted Answer

We need to use the formula for the difference quotient:
$$\frac { f ( a + h ) - f ( a ) } { h } = \frac { (a+h)^2 - 5(a+h) + 2 - (a^2 - 5a + 2) } { h }$$
Simplifying the numerator, we get:
$$\frac { 2ah + h^2 -5h } { h }$$
Factoring out an h from the numerator, we get:
$$\frac { h (2a + h - 5) } { h }$$
Canceling the h's, we are left with:
$$2a + h - 5$$
Therefore, the answer is choice B.

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Find $\frac { f ( a + h ) - f ( a ) } { h }$