022 Exam 2 Sample A, Problem 8

Use differentials to approximate the change in profit given $x=10$  units and $dx=0.2$  units, where profit is given by $P(x)=-4x^{2}+90x-128$.

Foundations:
A differential is a method of approximating a change,
$\int x^{n}dn={\frac {x^{n+1}}{n+1}}+C$
For setup of the problem we need to integrate the region between the x - axis, the curve, x = 1, and x = 4.

 Solution:

Step 1:

Step 2:

Return to Sample Exam