Home
Class 12
MATHS
Consider, f (x) is a function such that ...

Consider, f (x) is a function such that `f(1)=1, f(2)=4 and f(3)=9`
Statement 1 : `f''(x)=2" for some "x in (1,3)`
Statement 2 : `g(x)=x^(2) rArr g''(x)=2, AA x in R`

A

Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) be a function such that f(x)*f(y)=f(x+y),f(0)=1,f(1)=4. If 2g(x)=f(x)*(1-g(x))

If f:R rarr R be a function such that f(x+2y)=f(x)+f(2y)+4xy, AA x,y and f(2) = 4 then, f(1)-f(0) is equal to

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0

Consider the function f(x)=(.^(x+1)C_(2x-8))(.^(2x-8)C_(x+1)) Statement-1: Domain of f(x) is singleton. Statement 2: Range of f(x) is singleton.

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? f'(x)=2AA x in(1,3)f'(x)=f(x)=5 for some x in(2,3)f'(x)=3AA x in(2,3)f'(x)=2 for some x in(1,3)

Let f_(1):R rarr R and f_(2):C rarr C are two functions such that f_(1)(x)=x^(3) and f_(2)=x^(3) .Prove that f_(1) and f_(2) are not same.

Consider the function f(x)=(.^(x+1)C_(2x-8))(*^(2x-8)C_(x+1)) statement -1: Domain of f(x) is singleton.Statement -2: Range of f(x) is singleton.

Statement-1: Function f(x)=sin(x+3 sin x) is periodic . Statement-2: If g(x) is periodic then f(g(x)) periodic