Study of a parametric function I would like to study this function for x &#x2265;<!-- ≥ -->

Jordon Haley 2022-05-14 Answered
Study of a parametric function
I would like to study this function for x 0, b , d R :
y = b + d x 1 b d x
Can I say that it is monotone increasing (decreasing) over x in its domain for d > 0 ( d < 0)?
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Answers (2)

Kharroubip9ej0
Answered 2022-05-15 Author has 10 answers
Step 1
Note that x [ b + d x 1 b d x ] = d ( 1 b d x ) 2
Step 2
and hence the function is monotone increasing (decreasing) for d > 0 ( d < 0).
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Dominick Blanchard
Answered 2022-05-16 Author has 5 answers
Explanation:
By the quotient rule we get after simplifications for the first derivative y = d ( d x + b 1 ) 2
Step 2
Now you can consider the cases d > 0 or d < 0
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