Chapter 2.1, Problem 83AYU

To determine

To find:The value of $A$ if $f\left(2\right)=5$ .

Answer to Problem 83AYU

The value of $A$ is $-\frac{7}{2}$ .

Explanation of Solution

Given information:

A function $f\left(x\right)$ is given as $f\left(x\right)=2x^3+A{x}^2+4x-5$ .

Calculation:

Consider the given function,

  $f\left(x\right)=2x^3+A{x}^2+4x-5$

Substitute 2 for x in the above function.

  $\begin{array}{c}f\left(2\right)=2{\left(2\right)}^3+A{\left(2\right)}^2+4\left(2\right)-5\\ =2\times 8+4A+8-5\\ =16+4A+8-5\\ =19+4A\end{array}$

Now, $f\left(2\right)=5$

  $\begin{array}{c}19+4A=5\\ 4A=5-19\\ 4A=-14\\ A=-\frac{7}{2}\end{array}$

Hence, value of Ais $-\frac{7}{2}$ .