Approximate Changes (Calculus) - Need right Answer

I am unable to get the right answer, closest answer : -0.01(r-1)

Trying again and again it keeps raising a lot more of other questions, that is simply boring for me.

Would be more than grateful if someone could kindly show me a detailed steps to the solution please.

(JF Talbert Textbook, Exercise 16D, Q.22)

For the function A=1/(r-1)^2 , a small change in r when r=2(r-1)^2 produces a 2% reduction in the value of A.

Find the approximate change in r.

(Given Answer: 0.01 increase)

Re: Connected Rates Of Change (Calculus) - Need an Answer.

when , or

note: any info given on the range of values for r ?

for ...

... a decrease in r at 1/8 of a percent

for ...

there is your 1% increase in r

Re: Connected Rates Of Change (Calculus) - Need an Answer.

Thank you so much for that help.

you put an end to my day of agony and open a day of paradise :)

Re: Connected Rates Of Change (Calculus) - Need an Answer.

I have reviewed the problem, it comprises of 3 stages:

I. Solving for from , gives

II. Solving for from , gives:

III. And finally, Solving for from , that is a) or b)

Having given,

Therefore,

a) When

(increasing) (Happy)

b) when

(decreasing) (Wondering)

**********************

Sir, hope you take into consideration stage II. that lead to a different solution. :)