Consider a function \(f(x) = 1 – |x| on –1 ≤ x ≤ 1\). The value of \(x\) at…
2015
Consider a function \(f(x) = 1 – |x| on –1 ≤ x ≤ 1\). The value of \(x\) at which the function attains a maximum and the maximum value of the function are:
- A.
0, –1
- B.
–1, 0
- C.
0, 1
- D.
–1, 2
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Correct answer: C
Key idea: |x| is always nonnegative, so 1 − |x| is largest when |x| is smallest.
Step 1: |x| ≥ 0 for all x, and |x| = 0 only at x = 0.
Step 2: Evaluate f at x = 0: f(0) = 1 − |0| = 1.
Step 3: Check endpoints: f(1) = f(−1) = 1 − 1 = 0, which are smaller than 1.
Conclusion: The maximum value is 1, attained at x = 0.
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