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# Verify rolles theorem for function f(X)=2x^3+x^2-4x-2 in interval[-√3,√3]

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( – $\sqrt$3) = – 6$\sqrt$3 + 3 +4$\sqrt$3 – 2 = – 2$\sqrt$3 +1
f($\sqrt$3) = 6$\sqrt$3 + 3 – 4$\sqrt$3 – 2 = 2$\sqrt$3 +1
but here f( – $\sqrt$3) is not equal to f($\sqrt$3)
hence rolles theorem can’t be applied
I tink question is posted wrong.