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

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Answer 1 · 2018-05-07T09:26:41

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

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]}

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

Determine whether 3x^3 - 6x^2+5x-123x^3 - 6x^2+5x-12 is an increasing function, a decreasing function or neither?