Home
Class 12
MATHS
Let f(x) be a twice differentiable funct...

Let `f(x)` be a twice differentiable function for all real values of `x` and satisfies `f(1)=1,f(2)=4,f(3)=9.` Then which of the following is definitely true? (a).`f''(x)=2AAx` in (1,3) (b) `f''(x)= 5` for some x in (2,3) (c) `f''(x)=3AAx` in (2,3) (d) `f''(x)=2` for some x in (1,3)

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a) f^('')=2AAx in (1,3) (b) f^('')=f(x)=5forsom ex in (2,3) (c) f^('')=3AAx in (2,3) (d) f^('')=2forsom ex in (1,3)

If f(x) is a twice differentiable function and given that f(1)=2,f(2)=5 and f(3)=10 then

if f(x) be a twice differentiable function such that f(x) =x^(2) " for " x=1,2,3, then

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

Let f(x) be a twice-differentiable function and f"(0)=2. The evaluate: ("lim")_(xvec0)(2f(x)-3f(2x)+f(4x))/(x^2)

Let f: R->R be a function defined by f(x+1)=(f(x)-5)/(f(x)-3)AAx in R . Then which of the following statement(s) is/are true?

if f(x) is differentiable function such that f(1) = sin 1, f (2)= sin 4 and f(3) = sin 9, then the minimum number of distinct roots of f'(x) = 2x cosx^(2) in (1,3) is "_______"

Let f:[0,1]rarrR be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ?

Let f(x)=1-x-x^3 .Find all real values of x satisfying the inequality, 1-f(x)-f^3(x)>f(1-5x)

Let f(x)=1-x-x^3 .Find all real values of x satisfying the inequality, 1-f(x)-f^3(x)>f(1-5x)