Chapter 6.5, Problem 89STP

To determine

To graph:the given polynomial. Estimate the x -coordinate at which the relative maxima and relative minima occur.

Answer to Problem 89STP

Maxima occurs at $x=-0.51$ and relative minima occurs at $x=1.483$ .

Explanation of Solution

Given:

The given function is $f\left(x\right)=-3x^3+6x^2+2x-1$ .

Calculation:

As the given function is $f\left(x\right)=-3x^3+6x^2+2x-1$ .

Now, draw the graph of the given function.

  

From the graph, the point on the coordinates is $\left(1.483,5.377\right),\left(-0.519,0\right),\left(0.288,0\right),\left(0.232,0\right),\left(-0.15,-1.155\right),,\left(0,-1\right)$

Therefore, the maxima points occur at the x -coordinate at $x=-0.51$ which the relative minima occur at $x=1.483$

Hence, the x -coordinate at which the relative maxima occurs at $x=-0.51$ and relative minima occurs at $x=1.483$ .