Chapter SH, Problem 5.9EP

To determine

Find the value of the function at the given points.

Answer to Problem 5.9EP

The values of the function at the given points $p\left(-2\right)=8$ and $p\left(4\right)=-208$ .

Explanation of Solution

Given:

The given function is $p\left(x\right)=-3x^3-x^2+2x-8$ . The given points are $p\left(-2\right)$ and $p\left(4\right)$ .

Calculation:

  $p\left(x\right)=-3x^3-x^2+2x-8$

Substitute the value of $x=-2$ in the given function.

  $\begin{array}{l}p\left(-2\right)=-3{\left(-2\right)}^3-{\left(-2\right)}^2+2\left(-2\right)-8\\ =24-4-4-8\\ =24-16\\ =8\end{array}$

Substitute the value of $x=4$ in the given function.

  $\begin{array}{l}p\left(4\right)=-3{\left(4\right)}^3-{\left(4\right)}^2+2\left(4\right)-8\\ =-192-16+8-8\\ =8-216\\ =-208\end{array}$

Hence the values of the function at the given points $p\left(-2\right)=8$ and $p\left(4\right)=-208$ .