practice _prof. test #1 score: 15/17 answered: 16/17 question 17 given the function f(x)= - 3 + 3x²…

Explanation:

Step1: Find $f(a)$

Substitute $x = a$ into $f(x)=-3 + 3x^{2}$. $f(a)=-3 + 3a^{2}$

Step2: Find $f(a + h)$

Substitute $x=a + h$ into $f(x)=-3 + 3x^{2}$. $f(a + h)=-3+3(a + h)^{2}=-3+3(a^{2}+2ah+h^{2})=-3 + 3a^{2}+6ah+3h^{2}$

Step3: Find $\frac{f(a + h)-f(a)}{h}$

First, find $f(a + h)-f(a)$: $f(a + h)-f(a)=(-3 + 3a^{2}+6ah+3h^{2})-(-3 + 3a^{2})=6ah+3h^{2}$ Then divide by $h$: $\frac{f(a + h)-f(a)}{h}=\frac{6ah+3h^{2}}{h}=6a + 3h$

Answer:

$f(a)=-3 + 3a^{2}$ $f(a + h)=-3 + 3a^{2}+6ah+3h^{2}$ $\frac{f(a + h)-f(a)}{h}=6a + 3h$