Verified Solution • 2025–26 Session
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QJEEM20Macbef: JEE Main 2020 Mathematics - Class 12 JEEM20Macbef Solution: For all twice differentiable functions f : R R, with f(0) =…
For all twice differentiable functions f : R R,
with f(0) = f(1) = f'(0) = 0
with f(0) = f(1) = f'(0) = 0
Multiple Choice Options
- A f''(x) 0, at every point x (0, 1)
- B f''(x) = 0, for some x (0, 1)
- C f''(0) = 0
- D f''(x) = 0, at every point x (0, 1)
Step-by-Step Verified Solution
f : R R, with f(0) = f(1) = 0
and f'(0) = 0
f(x) is differentiable and continuous
and f(0) = f(1) = 0
Applying Rolle’s theorem in [0, 1] for function f(x)
f'(c) = 0, c (0, 1)
Now again
f'(c) = 0, f'(0) = 0
again applying Rolles theorem in [0, c] for function f'(x)
f''(c1) = 0 for some c1 (0, c) (0, 1)
and f'(0) = 0
f(x) is differentiable and continuous
and f(0) = f(1) = 0
Applying Rolle’s theorem in [0, 1] for function f(x)
f'(c) = 0, c (0, 1)
Now again
f'(c) = 0, f'(0) = 0
again applying Rolles theorem in [0, c] for function f'(x)
f''(c1) = 0 for some c1 (0, c) (0, 1)