Answer to Question #145753 in Algebra for liam donohue

Question

The function f(x)=2x3−24x2+72x−6 has two critical values. The smaller one equals
and the larger one equals

Answer 1

f(x) = 2x³-24x²+72x-6

Find the derivative of f(x) with respect to x.

f'(x) = 6x²-48x+72

Equate the derivative to zero.

0 = 6x²-48x+72

0 = x²-8x+12

0 = x²-6x-2x+12

0 = x(x-6)-2(x-6)

0 = (x-6)(x-2)

(x-6) = 0 or (x-2) =0

Therefore, x = 6 or x = 2.

Smaller critical value = 2

Larger critical value = 6