SOLUTION: Find an interval over which the functio F(x)=-(x+5)^2(x-4)^3 is decreasing.

Question 1108325: Find an interval over which the functio
F(x)=-(x+5)^2(x-4)^3 is decreasing.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
-(x+5)^2(x-4)^3
derivative is 2(x+5)(-1)(x-4)^3+3(x-4)^2*-(x+5)^2
The minus signs cancel and set equal to 0.
2(x+5)(x-4)^3+3(x-4)^2(x+5)^2=0
at x=-5 or x=4, the derivative has a critical point.
there should be one more.
2(x+5)(x-4)^3=-3(x-4)^2*2(x+5)^2
2(x-4)^3=-3(x-4)^2*2(x+5)
2(x-4)=-3*2(x+5)
2X-8=-6X-30
8x=-22
x=-22/8
Graphing is a good way to see it.

Without the graph, one can look at extreme values. As x becomes more negative, then it is minus the square* minus^3, and that is positive. So from x going from -oo to -5, the function is decreasing.
As x gets large positive, it is decreasing, so from -22/8 ( a local maximum), to +oo, it is decreasing.

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