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
Answer:
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
