Evaluate the difference quotient for the function. $$f ( x ) = 4 x ^ { 2 } - 5$$
A) $\quad 8 x + 4 h$
B) 1
C) $\quad 8$
D) $4 x + h$
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 and simplify:

$$\frac{(4(x+h)^2-5)-(4x^2-5)}{h} = \frac{8xh+4h^2}{h}$$

Simplify further to get:

$$8x + 4h$$

Therefore, the correct choice is A, which matches this expression.

Evaluate the Difference Quotient for the Function f(x)=4x2−5f ( x ) = 4 x ^ { 2 } - 5f(x)=4x2−5