Question

Solve the following question:

Answer 1

x = 2, x = 8

Explanation:

reminder that f'(x) =
`m_(tangent)`

Differentiate f(x) term by term using the power rule

`(d)/(dx)` (a
`x^(n)` ) = na
`x^(n-1)`

f(x) =
`(1)/(3)` x³ - 5x² + 2x + 10

f'(x) = x² - 10x + 2

Equating f'(x) to - 14

x² - 10x + 2 = - 14 ( add 14 to both sides )

x² - 10x + 16 = 0 ← in standard form

(x - 2)(x - 8) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 8 = 0 ⇒ x = 8