Find the range of values of x for which the function defined by f(x)= {2x}^(3) - {3x}^(2) + 12x is an increasing function. ​

Question

Find the range of values of x for which the function defined by f(x)=


`{2x}^(3) - {3x}^(2) + 12x`
is an increasing function.
​

Answer 1

all values! x ∈ R

Explanation:

The derivative f'(x) = 6x²-6x+12 is a parabola opening upward, with its (positive!) minimum at (0.5, 11.5). If the derivative is always positive, the function must be increasing everywhere!