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

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)