posted by Mira on .
How many critical points does the function:
(x+2)^5 * (x-3)^4
How would I solve this quickly? The answer says something about an effect of multiplicity of the zeros of the function?
A critical point of a function within its domain is any point which is not differentiable or when its derivative is zero.
f(x)=(x+2)^5 * (x-3)^4
is a polynomial, its domain is (-∞,∞) and differentiable throughout.
The only critical points are when the derivative is zero.
which factors to:
We see that
x=3 (multiplicity 3)
x=-2 (multiplicity 4)
So there is a total of 3+4+1 = 8 critical points, out of which there are 3 distinct points.