Study of a parametric functionI 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 &gt; 0 ( d &lt; 0)?

Question

Study of a parametric functionI 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  &amp;gt;  0 (  d  &amp;lt;  0)?

Kharroubip9ej0 · Accepted Answer

Step 1Note that       ∂          ∂      x            [                  b        +        d        x                    1        −        b        −        d        x              ]    =      d                  (        1        −        b        −        d        x        )                    2             Step 2and hence the function is monotone increasing (decreasing) for   d  &amp;gt;  0 (  d  &amp;lt;  0).

Dominick Blanchard · Accepted Answer

Explanation:By the quotient rule we get after simplifications for the first derivative       y    ′    =      d          (      d      x      +      b      −      1              )        2             Step 2Now you can consider the cases   d  &amp;gt;  0 or   d  &amp;lt;  0

Study of a parametric function I would like to study this function for x ≥

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