Question

Determine whether `3x^3 - 6x^2+5x-12` is an increasing function, a decreasing function or neither?

Answer 1

`color(maroon)(It's an increasing function"`

Explanation:

A function is "increasing" when the y-value increases as the x-value increases.

`color(crimson)("If f′(x) > 0, then f is increasing on the interval, and if f′(x) < 0, then f is decreasing on the interval."`

`f(x) = 3x^3 - 6x^2 + 5x - 12`

`f'(x) = 9x^2 -12x + 5 > 0 for all values of x`

graph{3x^3-6x^2+5x-12 [-10, 10, -5, 5]}

`"It's an increasing function as xan be seen from the graph too"`