In Problems 53– 60, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

$f\left(x\right)=0.25x^4+0.3x^3-0.9x^2+3(-3,2)$

The given function is:

$f\left(x\right)=0.25x^4+0.3x^3-0.9x^2+3(-3,2)$

The required graph is shown below:

A function $f$ has a local maximum at cif there is an open interval I containing c so that for all xin I , $f\left(x\right)\le f\left(c\right)$. We will call $f\left(c\right)$a local maximum value of $f$.

A function has a local minimum at cif there is an open interval I containing c so that, for all xin I , $f\left(x\right)\ge f\left(c\right)$. We call $f\left(c\right)$a localminimum value of $f$.

From the graph that we have drawn, we can see that $f$has local maximum at point $(0,3)$.

Here $f\left(x\right)<f\left(0\right)$.

Therefore, the local maximum is $f\left(0\right)=3$.

From the graph that we have drawn, we can see that $f$has a local minimum at $(-1.87,0.95)$.

Here $f\left(x\right)>f(-1.87)$.

The local minimum is$f(-1.87)=0.95$.

$f$also has a local minimum at $(0.97,2.65)$.

Here $f\left(x\right)>f(0.97)$.

The local minimum is$f(0.97)=2.65$.

We can see from the graph that the function is increasing from the point $(-1.87,0.95)$to $(0,3)$and from $(0.97,2.65)$to $(2,5.8)$.

So we can conclude from it that $f$is increasing on the intervals $(-1.87,0)$to $(0.97,2)$.

We can see from the graph that the function is decreasing on the intervals role="math" localid="1646041150746" $(-3,-1.87)$and role="math" localid="1646041197502" $(0,0.97)$.