Application of DerivativeHard
Question
If x1 and x2 are abscissa of two points on the curve f(x) = x - x2 in the interval [0, 1], then maximum value of the expression (x1 + x2) - (x12 + x22) is
Options
A.1/2
B.1/4
C.1
D.2
Solution
Maximum of f(x) is 1/4
Given expression is f(x1) + f(x2)
⇒ f(x1) ≤ 1/4 ⇒ f(x2) ≤ 1/4 ⇒ f(x1) + f(x2) ≤ 1/2
Given expression is f(x1) + f(x2)
⇒ f(x1) ≤ 1/4 ⇒ f(x2) ≤ 1/4 ⇒ f(x1) + f(x2) ≤ 1/2
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