F (x) = - x^2+12x + 3

a. find f (-2)

b. Find derivative f' (x)

f (-2) is - 25 and f' (x) is - 2x + 12

Step-by-step explanation:

Step 1:

Given f (x) = - x² + 12x + 3, find f (-2).

f (-2) = - (-2) ² + 12 (-2) + 3

= - (4) - 24 + 3 = - 28 + 3 = - 25

Step 2:

Find f' (x)

f' (x) = d/dx (-x² + 12x + 3) = - 2x + 12

Step-by-step explanation:

Given the function,

F (x) = - x^2+12x + 3

a) to determine f ( - 2), we would substitute x = - 2 into the given function. It becomes

F ( - 2) = - ( - 2) ^2 + 12 ( - 2) + 3

F ( - 2) = - 4 - 24 + 3

F ( - 2) = - 25

b) to find derivative f' (x), we would different the given function with respect to x. Recall

If y = x^n

dy/dx = nx^n - 1

Therefore,

f' (x) = - 2x^ (2 - 1) + 1 * 12x^1 - 1) + 0 * 3^ (0 - 1)

f' (x) = - 2x + 12x^0 + 0

f' (x) = - 2x + 12