Home
Class 12
MATHS
If f(x) is twice differentiable and f^('...

If f(x) is twice differentiable and `f^('')(0) = 3`, then `lim_(x rarr 0) (2f(x)-3f(2x)+f(4x))/x^(2)` is

Text Solution

Verified by Experts

The correct Answer is:
9
Promotional Banner

Topper's Solved these Questions

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos
  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|17 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

If graph of a function f(x) is shown in the adjacent figure, then Lim_(x rarr 0^(-)) [(4f(x)-6[f(x)])/(tan(2f(x)-6))] is equal to

If g(x)=(x^(3) - 2x + 4) f(x) and f(0) = 3 and lim(xrarr0) (f(x)-3)/x = 2 then g'(0) is:

Let f:RrarrR be such that f(a)=1, f(a)=2 . Then lim_(x to 0)((f^(2)(a+x))/(f(a)))^(1//x) is

If f(x) is differentiable and strictly increasing function, then the value of ("lim")_(xvec0)(f(x^2)-f(x))/(f(x)-f(0)) is 1 (b) 0 (c) -1 (d) 2

If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f(c)=-1,f(d)=2, f(e)=0 where a < b < c < d e, then the minimum number of zeroes of g(x) = f'(x)^2+f''(x)f(x) in the interval [a, e] is

If f(x) is the integral of (2 sin x-sin 2 x)/(x^(3)), "where x" ne 0, "then find" lim_(x rarr 0) f'(x) .

For every function f (x) which is twice differentiable , these will be good approximation of int_(a)^(b)f(x)dx=((b-a)/(2)){f(a)+f(b)} , for more acutare results for cin(a,b),F( c) = (c-a)/(2)[f(a)-f( c)]+(b-c)/(2)[f(b)-f( c)] When c= (a+b)/(2) int_(a)^(b)f(x)dx=(b-a)/(4){f(a)+f (b)+2 f ( c) }dx If lim_(t toa) (int_(a)^(t)f(x)dx-((t-a))/(2){f(t)+f(a)})/((t-a)^(3))=0 , then degree of polynomial function f (x) atmost is

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.