Question

Suppose that the function 'f' is differentiable at x=3 and lim h->0.. f(h) /h =1 , lim h->0 f(3+h) = 5. Find f(3) and f'(3). Such that F has property : f(x+y) = f(x) + f(y) + 3xy, for all values of x and y. ​

Answer 1

Answer:

As f(x) is differentiable at x=1

5=

h→0

lim

h

f(1+h)

assuming 0/0 form

Using L-hospital's rule,

5=

h→0

lim

1

f

′

(1)

∴ f

′

(1)=5