Find the maximum value of

Question

f(x) = -3x^2 + 12x-8

Answer 1

The function f(x) = -3x² + 12x  - 8

The maximum value of  f(x) then the derivative of f(x) = 0

f(x) = -3x² + 12x  - 8

Diferentiate each side with respective x

Recall :  From derivative formula d / dx(axⁿ) = ax^n-1

f¹(x) = 2(-3x^2-1) + 12x^1-1 -0

f¹(x) = -6x + 12(1)

f¹(x) = -6x + 12

Evaluate the maximum value of f(x) then the f¹(x) = 0

Substitute f¹(x) = 0

There fore 0 = -6x + 12

Add 6x to each side

6x = 6x -6x +12

6x = 12

Divide each side by 6

6x / 6 = 12 / 6

Simplify

x = 2

Substitute x = 2  to f(x) = -3x² + 12x - 8

f(2) = -3(2)²+ 12(2) - 8

f(2) = -12 +24 - 8

f(2) = -20 + 24

f(2) = 4

There fore the maximum value of  f(x) : f(2) = 4.