Home
Class 12
MATHS
Let f(x+y) = f(x). F(y) for all x and y....

Let f(x+y) = f(x). F(y) for all x and y. Suppose f(5) = 2 and f'(0) = 3. Find f'(5).

Text Solution

Verified by Experts

The correct Answer is:
6
`f(x+y)=f(x)f(y)" (1)"`
`f'(5)=underset(hrarr0)lim(f(5+h)-f(5))/(h)`
`=underset(hrarr0)lim(f(5)f(h)-f(5))/(h)`
`=f(5)underset(hrarr0)lim(f(h)-1)/(h)`
`=f(5)underset(hrarr0)lim(f(h)-1)/(h)`
In (1), replace x by 5 and y by 0. Then, `f(5+0)=f(5)cdotf(0)`
`"or "f(0)=1`
`"or "f'(5)=f(5)underset(hrarr0)lim(f(h)-f(0))/(h)`
`=f(5)f'(0)=2xx3=6`
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

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

f(x+y)=f(x).f(y) for all x,yinR and f(5)=2,f'(0)=3 then f'(5) is equal to

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 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.

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) be defined for all x > 0 and be continuous. Let f(x) satisfy f((4x)/y)=f(x)-f(y) for all x,y and f(4e) = 1, then (a) f(x) = In 4x(b) f(x) is bounded (c) lim_(x->0) f(1/x)=0 (d) lim_(x->0)xf(x)=0

If F :R to R satisfies f(x +y ) =f(x) + f(y) for all x ,y in R and f (1) =7 , then sum_(r=1)^(n) f(R ) is

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

f(x)+f(y)=f((x+y)/(1-xy)) ,for all x,yinR . (xy!=1) ,and lim_(x->0) f(x)/x=2 .Find f(1/sqrt3) and f'(1) .