Find the intervals in which the function `"f"("x")`=`"x"^"3"- "12"x^2+ "36"x"+"17" ` is (a) increasing, (b) decreasing.

Explanation

Here, `f(x) = x^3-12x^2+36x+17`


Now, `f'(x) = 3x^2-24x+36`

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

`=>f'(x) = 3((x-6)(x-2))`

A function is increasing if `f'(x) gt 0`.

A function is decreasing if `f'(x) lt 0`.

If `f'(x) lt 0`,

...