Question

Can someone help me solve question number 14? I've tried to solve it and got 3426 while the answers in the book say it's 2,6. Can someone pls explain why it's wrong?

Answer 1

x = 2, 6

Explanation:

differentiate f(x) using the power rule

f'(a
`x^(n)` ) = na
`x^(n-1)` and f'( constant) = 0

given

f(x) = x³ - 12x² + 6x - 8

f'(x) = 3x² - 24x + 6

equate f'(x) to - 30

3x² - 24x + 6 = - 30 ( add 30 to both sides )

3x² - 24x + 36 = 0 ( divide through by 3 )

x² - 8x + 12 = 0 ← in standard form

(x - 2)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 6 = 0 ⇒ x = 6

solution is x = 2, 6