Question

f(x) = (x-3)/(x+1)     find f'(0)f(x) = (x-3)/(x+1)     find f'(0)

Accepted Answer

f(x) = (x-3)/(x+1)
Let f(x) = u/v  such that:\
u= x-3  ==>   u' = 1
v= x+1  ==> v'= 1
f'(x) = (u'v- uv')/v^2
       = [1*(x+1) - (x-3)*1]/ (x+1)^2
       = (x+1 - x + 3)/ (x+1)^2
       = 4/(x+1)^2
f'(0) = 4/(0+1)^2 = 4/1 = 4
==> f'(0) = 4

Answer

You need to find derivative of function using the quotient rule such that:



You need to substitute 0 for x in f'(x) such that:

Hence, evaluating the derivative of the function at  yields

Answer

f(x) =   (x-3)/(X+1)       THEN   
by putting 0 on the value of x we get,
f(0)  =  (0-3)/(0+1)          
f(0)  =-3/1                               
f(0)   =-3

Answer

f(x) = (x-3) / (x+1)
As, x= 0
(plugging the values in the equation)
f(0) = (0-3) / (0+1)
f(0) = (-3) / (+1)
f(0) = -3

Answer

To calculate f'(0), we'll use the definition of the derivative:
f'(0) = lim {[f(x) - f(0)]/(x-0)} , x-->0
f'(0) = lim {[(x-3)/(x+1)  - (-3)/1]/ x},  x-->0
f'(0) = lim {[(x-3)/(x+1)  - (-3)/1]/ x},  x-->0
f'(0) = lim [(x-3 + 3x + 3)/ x(x+1)],  x-->0
We'll combine like terms:
f'(0) = lim [(x-3 + 3x + 3)/ x(x+1)],  x-->0
f'(0) = lim [4x/x(x+1)],  x-->0
f'(0) = lim [4x/x(x+1)],  x-->0
f'(0) = lim [4/(x+1)],  x-->0
f'(0) = lim [4/(x+1)],  x-->0
f'(0) = 4/(0+1) = 4/1 = 4

Answer

f(x) = (x-3)/(x+1)
To find f'(0).
Solution:
f(x) = (x+3)/(x+1) = [(x+1)- 4]/(x-1)
f(x) = (x+1)/(x+1) - 4/(x+1).
f(x) =  1 - 4/(x+1)
f'(x) = (1)' - {4/(x+1)}'
f'(x) = 0 - 4/(x+1)^2, as (constant)' = 0 and (k/(x+a)^n)'  = - kn/(x-a)^(n+1).
Therefore, f'(0) = -4/(0+1)^2 = -4.

Answer

Given:
f(x) = (x - 3)/(x + 1)
Let:
x - 3 = u
And
x + 1 = v
Then:
f(x) = u/v
And:
f'(x) = (u'v - uv')/(v^2)
u' = 1
v' = 1
Substituting values of u, v, u' and v' in equation for f"(x):
f'(x) = [1*(x + 1) - 1*(x - 3)]/[(x + 1)^2]
= (x + 1 - x + 3)/[(x + 1)^2]
= 4/[(x + 1)^2]
Therefore:
f'(0) = 4/[(0 + 1)^2
= 4/1 = 4
Answer:
f'(0) = 4

Math

f(x) = (x-3)/(x+1) find f'(0) f(x) = (x-3)/(x+1) find f'(0)

Expert Answers

We’ll help your grades soar

Related Questions

`f'''(x) = cos(x), f(0) = 1, f'(0) = 2, f''(0) = 3` Find `f`.

Find the function f such that `f'(x) = f(x)(1-f(x))` and `f(0) = 1/2`

`f(x) = x/(x^2 - x + 1), [0, 3]` Find the absolute maximum and minimum values of f on the given interval

Given f(x) and g(x), please find (fog)(X) and (gof)(x) f(x) = 2x g(x) = x+3

if f(x)=2x-3 and fg(x)=2x+1,find g(x)