Question

f(x)=x^2(x+5)^1/2 find the intervals in which f is decreasing and increasing

Answer 1

when the derivative y values are (+) then it is increasing, when (-) then decreasing

Answer 2

can u find exactly which ones?

Answer 3

yeah
you can simply do that by making a sign chart

Answer 4

ok so the intervals are -infinity to -5, -5 to 0, 0 to infinity

Answer 5

?

Answer 6

-5 isn't right. Those are just the points where the graph touches the x-axis. You need to find where the *derivative* changes sign.

Answer 7

\[f(x)=x^2\sqrt{x+5}\quad,\quad x\geq -5\]\[f'(x)=2x\sqrt{x+5}+x^2\frac{1}{2\sqrt{x+5}}=\frac{4x(x+5)+x^2}{2\sqrt{x+5}}\]\[f'(x)=\frac{5x(x+4)}{2\sqrt{x+5}}\]\[f'(x)>0:\quad -5<x<-4\quad\wedge\quad x>0\quad f(x)\uparrow\]\[f'(x)<0:\quad -4<x<0\quad f(x)\downarrow\]

Answer 8

@nikvist, Second-to-last line should be union, not intersection.