# Thread: Family of Functions!

1. ## Family of Functions!

let p(x) = x^3-ax, where a is constant

a.) if a<0, show that p(x) is alwayss increasing
b.) if a>0, show that p(x) has a local maximum and minimum
c.) sketch and label typical graphs for the cases when a<0 and when a>0

can i get some help with this one please, i just dont know what to do...thanks

mathlete

2. Originally Posted by mathlete
let p(x) = x^3-ax, where a is constant

a.) if a<0, show that p(x) is alwayss increasing
find the derivative, show that it will always be positive

b.) if a>0, show that p(x) has a local maximum and minimum
set the derivative you found in part (a) to 0 and solve for x. you will get two solutions. note that $\displaystyle a$ must be positive for the solutions to work.

c.) sketch and label typical graphs for the cases when a<0 and when a>0
it shouldn't be hard coming up with examples. just plug in a number for a>0 and graph that, then plug in a number for a<0 and graph that. the families of curves should all look familiar