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ID:
Class: 12
Subject: Math
Topic: Application of Derivative
Type: Short
Question:
Find the maximum and minimum values, if any, of the function \( f(x) = - (x - 1)^2 + 10 \)
Official Solution
Explanation:
We know:
\[
(x - 1)^2 \geq 0 \Rightarrow - (x - 1)^2 \leq 0
\Rightarrow f(x) = - (x - 1)^2 + 10 \leq 10
\]
Maximum value occurs when \(x = 1\):
\[
f(1) = - (1 - 1)^2 + 10 = 10
\]
No minimum value exists since the function decreases indefinitely.
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