a. for the function and point below, find f(a). b. determine an equation of the line tangent to the graph of…

a. for the function and point below, find f(a). b. determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. f(x)=3x² + 3x, a = - 2 a. f(a)=

a. for the function and point below, find f(a). b. determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. f(x)=3x² + 3x, a = - 2 a. f(a)=

Answer

Answer:

-3

Explanation:

Step1: Find the derivative of f(x)

Using the power - rule $(x^n)'=nx^{n - 1}$, if $f(x)=3x^{2}+3x$, then $f'(x)=(3x^{2}+3x)'=(3x^{2})'+(3x)'=3\times2x+3 = 6x + 3$.

Step2: Evaluate f'(a) at a = - 2

Substitute $x=a=-2$ into $f'(x)$. So $f'(-2)=6\times(-2)+3=-12 + 3=-3$.