Home
Class 12
MATHS
A function f(x) satisfies the relation f...

A function f(x) satisfies the relation `f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R`. If f'(0) = - 1, then

A

f(x) is a polynomial function

B

f(x) is an exponential function

C

f(x) is twice differentiable for all `x in R`

D

f'(3) = 8

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Promotional Banner

Similar Questions

Explore conceptually related problems

A function f : R to R satisfies the equation f(x+y) = f (x) f(y), AA x, y in R and f (x) ne 0 for any x in R . Let the function be differentiable at x = 0 and f'(0) = 2. Show that f'(x) = 2 f(x), AA x in R. Hence, determine f(x)

A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)| for all x,y in R. If f'(0) exists, prove that f'(x) exists for all x, in R.

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then The value of underset(x to -oo)(lim)f(x) is

The function f(x) satisfying the equation f^2 (x) + 4 f'(x) f(x) + (f'(x))^2 = 0

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

Consider function f(x) satisfies the relation f(x+y^(3))=f(x)+f(y^(3))AAx,yinRand differentiable for all x . Statement I If f'(2)=a then f'(-2)=a f(x) is an odd function.

A derivable function f : R^(+) rarr R satisfies the condition f(x) - f(y) ge log((x)/(y)) + x - y, AA x, y in R^(+) . If g denotes the derivative of f, then the value of the sum sum_(n=1)^(100) g((1)/(n)) is

If f(x) satisfies the relation, f(x+y)=f(x)+f(y) for all x,y in R and f(1)=5, then find sum_(n=1)^(m)f(n) . Also, prove that f(x) is odd.

Statement 1: If differentiable function f(x) satisfies the relation f(x)+f(x-2)=0AAx in R , and if ((d/(dx)f(x)))_(x=a)=b ,t h e n((d/(dx)f(x)))_(a+4000)=bdot Statement 2: f(x) is a periodic function with period 4.