Evaluate the difference quotient for the function. $$f ( x ) = 3 x ^ { 2 } - 20$$
A) 3
B) $\quad 1$
C) $\quad 6$
D) $\quad 3 x + h$
E) $\quad 6 x + 3 h$

Question

Quizplus · Accepted Answer

The difference quotient is given by the formula $\frac{f(x+h)-f(x)}{h}$. For $f(x) = 3x^2 - 20$, we calculate $f(x+h) = 3(x+h)^2 - 20 = 3(x^2 + 2xh + h^2) - 20 = 3x^2 + 6xh + 3h^2 - 20$. Subtracting $f(x) = 3x^2 - 20$ from this gives $3x^2 + 6xh + 3h^2 - 20 - (3x^2 - 20) = 6xh + 3h^2$. Dividing by $h$ gives $6x + 3h$, which corresponds to choice E.

Evaluate the Difference Quotient for the Function f(x)=3x2−20f ( x ) = 3 x ^ { 2 } - 20f(x)=3x2−20

Evaluate the Difference Quotient for the Function $f ( x ) = 3 x ^ { 2 } - 20$