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Verify rolle`s theorem for the function f(X)=2x^3+x^2-4x-2 in interval [-√3,√3]

Verify rolle`s theorem for the function f(X)=2x^3+x^2-4x-2 in interval [-√3,√3]

Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago
for rolle’s theorem,
  1. f(x) should be continuous in (a, b)
  2. f(x) should be diffrentiable in (a, b)
  3. if f(a)= f(b) then there exist a point c in(a, b) such that f’(c) = 0
 
now as we see that point 1 & point 2 is true.
now coming to the 3rd point
f( – \sqrt3) = – 6\sqrt3 + 3 +4\sqrt3 – 2 = – 2\sqrt3 +1
f(\sqrt3) = 6\sqrt3 + 3 – 4\sqrt3 – 2 = 2\sqrt3 +1
but here f( – \sqrt3) is not equal to f(\sqrt3)
hence rolles theorem can’t be applied

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