LaGrange's Mean Value theorem
Trending Questions
Q.
If f (x) is differentiable in the interval [2, 5], where f (2)=15 and f (5)=12, then there exists a number c, 2 < c < 5 for which f ' (c) is equal to
1/5
1/10
None of these
1/2
Q.
By LMVT, which of the following is true for x>1
1+x In x<x<1+In x
x <1 + x In x<1+In x <x
1+In x<x<1+x In x
1+In x <1+x In x<x
Q.
According to LMVT, if a function f(x) is continuous on [a, b] and differentiable on the interval (a, b) then which of the following option should be correct for some value c from the interval (a, b)?( c can take any value from the interval (a, b) )
None of the above
Q. If f and g are differentiable functions in [0, 1] satisfying f(0)=2=g(1), g(0)=0 and f(1)=6, then for some c ϵ ]0, 1[
- 2f′(c)=g′(c)
- f′(c)=g′(c)
- f′(c)=2g′(c)
- 2f′(c)=3g′(c)
Q. Let f be differentiable for all x. If f(1)=−2 and f (x)≥2 for all x∈(1, 6], then which of the following cannot be the value of f(6)?
- 9
- 10
- 6
- 7
- 8
Q. For the function f(x)=x+1x, x∈(1, 3], the value of c for which the Lagranges Mean Value Theorem holds is .
- 1
- √3
- 2
- √2