022 Exam 2 Sample A, Problem 8

Use differentials to approximate the change in profit given $x=10$  units and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle dx = 0.2}   units, where profit is given by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P(x) = -4x^2 + 90x - 128} .

Foundations:
A differential is a method of approximating a change,
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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:

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