Question

Let f(x) = 5 + 12x -x^3. Using the differentiation techniques learnt, find

a. The intervals on which f is increasing

Answer 1

Let $f(x) = 5 + 12x -x^3$. Using the differentiation techniques let us find the intervals on which $f$ is increasing. Since $f'(x)=12-3x^2=0$ implies $x=-2$ or $x=2,$ and $f'(x)>0$ for $x\in(-2,2),$ we conclude that the function $f$ is increasing on the interval $(-2,2).$