Answer:
Max Value: x = 400
General Formulas and Concepts:
<u>Algebra I</u>
- Domain is the set of x-values that can be inputted into function f(x)
<u>Calculus</u>
- Antiderivatives
- Integral Property:
- Integration Method: U-Substitution
- [Integration] Reverse Power Rule:
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Identify Variables</u>
<em>Using U-Substitution, we set variables in order to integrate.</em>
<u>Step 3: Integrate</u>
- Define:
- Substitute:
- [Integral] Int Property:
- [Integral] U-Sub:
- [Integral] Rewrite:
- [Integral - Evaluate] Reverse Power Rule:
- Simplify:
- Back-Substitute:
- Factor:
<u>Step 4: Identify Domain</u>
We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.
Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.