Question

Divide into intervals and evaluate to find the max/min.

f(x)= -(x-1)^2(x+4)
I pick -2
-(-2-1)^2(-2+4)=-18

Is that the correct answer

Answer 1

so, is -18 the max or the min?

There is a double root at x=1, where it just touches the x-axis.

It crosses the x-axis at x = -4

Since this is a cubic polynomial, with negative leading coefficient, it drops down from the left.

So, it is decreasing on (-∞,-4) and beyond to the minimum.

It comes back up the the x-axis at x=1, so there is a maximum there, as it drops back down.

It continues decreasing on (1,∞).

Somewhere in (-4,1) there is a minimum. In fact, there is a minimum at (-7/3, -500/27). So, the minimum value is -18.5

Why did you pick -2? Just a guess? Not a very useful strategy.