Question

question 6 let (f(x)=-3x^{2}+18x + 7). which of the following is (\frac{f(x + h)-f(x)}{h})? - ( - 3x^{2}-3h^{2}+18x + 18h+7) - ( - 6x-3h + 18) - ( - 6xh-3h^{2}+18h) - ( - 6x^{2}+36x + 14+h) - ( - 3x^{2}-6xh-3h^{2}+18x + 18h+7)

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)=-3x^{2}+18x + 7$.
$f(x + h)=-3(x + h)^{2}+18(x + h)+7=-3(x^{2}+2xh+h^{2})+18x + 18h+7=-3x^{2}-6xh-3h^{2}+18x + 18h+7$

Step2: Calculate $f(x + h)-f(x)$

$f(x + h)-f(x)=(-3x^{2}-6xh-3h^{2}+18x + 18h+7)-(-3x^{2}+18x + 7)$
$=-3x^{2}-6xh-3h^{2}+18x + 18h+7 + 3x^{2}-18x - 7=-6xh-3h^{2}+18h$

Step3: Calculate $\frac{f(x + h)-f(x)}{h}$

$\frac{f(x + h)-f(x)}{h}=\frac{-6xh-3h^{2}+18h}{h}=-6x-3h + 18$

Answer:

$-6x-3h + 18$