Find the intervals in which the function `f(x)=3/2x^4-4x^3-45 x^2+51` is (a) strictly increasing. (b) strictly decreasing.

Explanation

`f(x) = 3/2x^4-4x^3-45x^2+51`

`:. f'(x) = 6x^3-12x^2-90x`

So, for maximum or minimum, `f'(x)` should be `0`.

`:. 6x^3-12x^2-90x = 0`

`=>x(x^2-2x-15) = 0`

`=>x(x-5)(x+3) = 0`

`=>x = -3 and x = 0 and x = 5`

If we check, `f'(-4)`,

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