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Let f: R -> R be a differentiable functi...

Let `f: R -> R` be a differentiable function such that f (a) = 0 = f (b) and `f' (a) f '(b) gt 0` for some `a lt b`. Then the minimum number of roots of f'(x) 0 in the interval (a, b) is

A

3

B

2

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
`f'(a).f'(b) gt 0`
so either both are positive or both negative
`f(a) = f(b) = 0`
`f'(x) = 0`

`2` roots
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KVPY PREVIOUS YEAR-KVPY-exercise
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  8. Let's say abcde is a 5 digit number which when multiplied by 9 new num...

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  9. I: m is any composite number that divides (m-1)! II: n is a natural ...

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  14. If the function f(x) = 2+x^2-e^x and g(x) = f^(-1)(x), then the value ...

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  15. S= lim(nrarroo) sum(k=0)^n 1/sqrt(n^2 + k ^2)

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  16. f(x): R to R |f(x)-f(y)| > |x-y| forall x,y in R check one-one/man...

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  17. x^3 - [x]^3 = (x - [x])^3

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  18. S1:lim(n->oo) (2^n + (-2)^n)/2^n does not exist S2:lim(n->oo) (3^n +...

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