Let f(x)=x/(x+7) Find the greater and lesser values of x where f′(x)=6.

Question

the question is above, i need to find a greater and lesser value when f prime of x is at 6 of that equation!

Answer 1

f(x) = x / (x + 7)

f'(x)
= [(x + 7)(1) - (x)(1)] / (x + 7)^2
= [x + 7 - x] / (x + 7)^2
= 7 / (x + 7)^2

When f'(x) = 6, we have:

7 / (x + 7)^2 = 6
(x + 7)^2 = 7 / 6
x + 7 = sqrt(7/6) or = -sqrt(7/6)
x = -7 + sqrt(7/6) or x = -7 - sqrt(7/6)

Hence, the greater value is x = -7 + sqrt(7/6) and the lesser value is x = -7 - sqrt(7/6).