The sufficient conditions for the functi...

The sufficient conditions for the function `f,RtoR` to be maximum at x=a will be: a)`f'(a)gt0andf''(a)gt0` b)`f'(a)=0andf''(a)=0` c)`f'(a)=0andf''(a)lt0` d)`f'(a)gt0andf''(a)lt0`

A

`f'(a)gt0andf''(a)gt0`

B

`f'(a)=0andf''(a)=0`

C

`f'(a)=0andf''(a)lt0`

D

`f'(a)gt0andf''(a)lt0`

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

The function f(x)=ax+b is strictly increasing for all real x is a) agt0 b) alt0 c) a=0 d) ale0

In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f(0) must be defined as

In order that the function f(x) = (x+1)^(1/x) is continuous at x = 0, f(0) must be defined as

The function {:(f:R to R:f(x) = 1, if x gt 0),(" "= 0, if x =0),(" "=-1, if x lt0 is a):}

The value of f(0) so that the function f(x) = (log(sec^2 x))/(x sin x), x != 0 , is continuous at x = 0 is

If f(x) = x for x le 0 = 0 for x gt 0 , then f(x) at x = 0 is

The function f(x)=x/(1+|x|) is differentiable in: a) x in R b) x=0 only c) xlt0 d) xgt0

If for a function f(x),f'(a)=0,f"(a)=0,f'''(a)gt0, then at x=a,f(x) is a)Minimum b)Maximum c)Not an extreme point d)Extreme point