Consider the points $A$ and $C$ are on $y=x^p$. We are told that point $A$ has coordinates $( a, b )$, where $0<a<1$ and point $C$ has coordinates $( c, d )$, where $1<c$.
Give a convincing argument that $b+d$ must be greater than $1$.Two points on the graph of $y=kx^p$ are labeled $A$ and $C$. Point $A$ has coordinates $(a,b)$, where $0<a<1$ and point $C$ has coordinates $(c,d)$, where $1<c$.
If we are told that that the product $k\cdot p$ is negative, what can be concluded about the points $A$ and $C$? Defend your answer.
I can't figure it out. Can someone help. I don't know where to start
Hints: For 1, consider what happens depending on the sign of $p$. If I tell you $p \lt 0$, what can you conclude?
For 2, what can you say about the sign of $\frac {dy}{dx}?$ Does that let you say something interesting about $b,d?$