Question

Is `f(x)=(2x+3)(x-6)(x-2)` increasing or decreasing at `x=-2`?

Answer 1

increasing at x = -2

Explanation:

To find if f(x) is increasing/decreasing , require to differentiate the function.

• If f'(x) > 0 then f(x) is increasing
• If f'(x) < 0 then f(x) is decreasing

before differentiating , distribute the brackets , beginning with the 1st 'pair'

`(2x+3)(x-6) = 2x^2 -9x - 18`

now `(2x^2 - 9x - 18 )(x - 2 )color(black)(" to complete the expansion ")`

`= 2x^3 - 4x^2 - 9x^2 + 18x - 18x + 36 = 2x^3 - 13x^2 + 36`

`rArr f'(x) = 6x^2 - 26x`

`f'(-2) = 6(-2)^2 -26(-2) = 24 + 52 =76`

since f'(-2) > 0 , f(x) is increasing at x = -2