# 022 Exam 2 Sample A, Problem 8

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

Foundations:
A differential is a method of approximating a change,
${\displaystyle \int x^{n}dn={\frac {x^{n+1}}{n+1}}+C}$
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: