Home
Class 12
MATHS
Let f be a function such that f(x+y)=f(x...

Let `f` be a function such that `f(x+y)=f(x)+f(y)` for all `xa n dya n df(x)=(2x^2+3x)g(x)` for all`x ,` where `g(x)` is continuous and `g(0)=3.` Then find `f^(prime)(x)dot`

Text Solution

Verified by Experts

The correct Answer is:
9
`f'(x)=underset(hrarr0)lim(f(x+h)-f(x))/(h)`
`=underset(hrarr0)lim(f(x)+f(h)-f(x))/(h)`
`=underset(hrarr0)lim(f(h))/(h)`
`=underset(hrarr0)lim((2h^(2)+3h)g(h))/(h)`
`=underset(hrarr0)lim(2h+3)g(h)`
`=(0+3)g(0)`
`=3g(0)`
`=3xx3`
`=9`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Single)|137 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.8|15 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If for a function f : R to R f (x +y ) =F(x ) + f(y) for all x and y then f(0) is

Let f:R->R be a continuous function such that |f(x)-f(y)|>=|x-y| for all x,y in R ,then f(x) will be

A function f:RtoR is such that f(x+y)=f(x).f(y) for all x.y inR and f(x)ne0 for all x inR . If f'(0)=2 then f'(x) is equal to

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)(0)=3. Find f^(prime)(5)dot

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

A function f: RvecR satisfies the equation f(x+y)=f(x)f(y) for all x , y in Ra n df(x)!=0fora l lx in Rdot If f(x) is differentiable at x=0a n df^(prime)(0)=2, then prove that f^(prime)(x)=2f(x)dot

Let f: RvecR be a function satisfying condition f(x+y^3)=f(x)+[f(y)]^3 for all x ,y in Rdot If f^(prime)(0)geq0, find f(10)dot

If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N such that f(1) = 3 and sum _(x=1)^nf(x)=120 , find the value of n.