For every $1 the students raise for the new playground equipment fund, the parents association donates $10 to the fund. If the x
1 answer:
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Answer:
D. 3x²
General Formulas and Concepts:
<u>Algebra II</u>
- If you raise e to the natural log, they cancel out and vice versa
<u>Calculus</u>
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
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<u>Step 2: Rewrite</u>
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<u>Step 3: Take Derivative</u>
- Basic Power Rule: f'(x) = 3x³⁻¹
- Simplify: f'(x) = 3x²
We're minimizing 
subject to 
. Using Lagrange multipliers, we have the Lagrangian
with partial derivatives
Set each partial derivative equal to 0:
Subtracting the second equation from the first, we find
Similarly, we can determine that
and 
by taking any two of the first three equations. So if 
determines a critical point, then
So the smallest value for the sum of squares is
when 
.
with partial derivatives
Set each partial derivative equal to 0:
Subtracting the second equation from the first, we find
Similarly, we can determine that
So the smallest value for the sum of squares is