Chapter 6.6, Problem 84SR

To determine

The value of $p\left(-4\right)\text{and }p\left(x+h\right)$ for the function $p\left(x\right)=2x^3-1$ .

Answer to Problem 84SR

The value of $p\left(-4\right)\text{and }p\left(x+h\right)$ are $-129$ and $2\left(x^3+h^3+3x^{2}h+3x{h}^2\right)-1$ respectively.

Explanation of Solution

Given information: The given function is,

  $p\left(x\right)=2x^3-\mathrm{1......}\left(1\right)$

Calculation: The value of $p\left(-4\right)\text{and }p\left(x+h\right)$ can be evaluated using (1) as,

  $\begin{array}{c}p\left(-4\right)=2{\left(-4\right)}^3-\mathrm{1......}\left(\text{Pluggingy }x=-4\right)\\ =-128-1\\ =-129\\ \text{And, }p\left(x+h\right)=2{\left(x+h\right)}^3-\mathrm{1......}\left(\text{Pluggingy }x=x+h\right)\\ =2\left(x^3+h^3+3x^{2}h+3x{h}^2\right)-1\end{array}$