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QJEEM20Ma5488: JEE Main 2020 Mathematics - Class 12 JEEM20Ma5488 Solution: Let f : R R be a function defined by f(x) = max {x, x 2 }. Let…
Let f : R R be a function defined by
f(x) = max {x, x2}. Let S denote the set of all points in R, where f is not differentiable. Then :
f(x) = max {x, x2}. Let S denote the set of all points in R, where f is not differentiable. Then :
Multiple Choice Options
- A {0, 1}
- B {0}
- C (an empty set)
- D {1}
Step-by-Step Verified Solution
From graph you can see,
(1) when x < 0 then y = x2 is greater than y = x. That is why for f(x) that curved part is chosen.
(2) when 0 x < 1 then y = x is greater than y = x2. That is why for f(x) part of that straight line is chosen.
(3) when x 1 then y = x2 is greater than y = x. That is why for f(x) that curved part is chosen.
Here on the graph of f(x) there is two sharp corner at x = 0 and x = 1. As we know no function is differentiable at the sharp corner. So f(x) is not differentiable at those two sharp corner.