Home
Class 12
MATHS
Suppose that f(x) is a differentiable fu...

Suppose that f(x) is a differentiable function such that f'(x) is continuous, `f'(0)=1` and `f''(0)` does not exist. Let `g(x)=xf'(x)`. Then-

A

g'(0) does not exist

B

`g'(0)=0`

C

`g'(0)=1`

D

`g'(0)=2`

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1) =1 , then

Let f:(0,oo)toRR be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in(0,oo) and f(1)ne1 . Then-

Let f:Rto R be a twice continuously differentiable function such that f(0)=f(1)=f'(0)=0 . Then

Let f(x) be a derivable function f'(x)gtf(x)" and " f(0)=0 . Then

Let f(x) be differentiable for real such that f'(x)lt0" on "(-4,6) and f(x) gt 0" on "(6,oo). If g(x)=f(10 - 2x) , then the value of g'(2) is

Let f be a twice differentiable function such that f"(x) = -f(x) , and f'(x) = g(x) , h(x)=[f(x)]^2+[g(x)]^2 Find h(10), if h(5) = 11

Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(4)=1, f(0) = -1 and f'(0) =1 If, g(x)=(f(2f^(2)(x)+2))^(2), then g'(0) equals

Let f:RR to(0,oo)" and "g:RR to RR be twice differentiable functions such that f'' and g'' are continuous functions on RR . Suppose f'(2)=g(2)=0,f''(2)ne0 and g'(2)ne0 . If underset(x to2)lim(f(x)g(x))/(f'(x)g'(x))=1 . Then

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then lim_(x->0)(f(x)-1)/x is a. 1//2 b. 1 c. 2 d. 0