Question

F(x)= -x^2+12x + 3
a. find f(-2)
b. Find derivative f’(x)

Answer 1

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

Answer 2

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

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