Friday

January 30, 2015

January 30, 2015

Posted by **Mira** on Friday, April 22, 2011 at 11:03pm.

(x+2)^5 * (x-3)^4

have?

How would I solve this quickly? The answer says something about an effect of multiplicity of the zeros of the function?

- calculus -
**MathMate**, Friday, April 22, 2011 at 11:15pmA critical point of a function within its domain is any point which is not differentiable or when its derivative is zero.

Since

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.

f'(x)=0 =>

4(x-3)^3(x+2)^5+5(x-3)^4(x+2)^4=0

which factors to:

(x-3)^3*(x+2)^4*(9*x-7)=0

We see that

x=3 (multiplicity 3)

x=-2 (multiplicity 4)

and

x=7/9

So there is a total of 3+4+1 = 8 critical points, out of which there are 3 distinct points.

**Answer this Question**

**Related Questions**

Algebra - Find all of the zeros of the polynomial function and state the ...

calculus - Using a graphing utility, graph and approximate the zeros and their ...

Algebra - Please help. Having a hard time with this. Find all of the zeros of ...

Algebra - Find all of the zeros of the polynomial function and state the ...

Calculus - I'm doing test corrections, and it's been a few weeks since we did ...

Algebra - Find all of the zeros of the polynomial function and state the ...

Math - I just wanted to double check that I am correct. 1.Find the zeros for the...

derivative am i right or wrong - what is the antiderivative of 1/(x^2-2x+2)? ...

Calculus - How many critical points does the function f(x) = [(x-2)^5][(x+3)^4] ...

Math - Consider the function y = 3x5 – 25x3 + 60x + 1. Find the critical points ...