Thread: determining loca max and minimum point without graphing (polynomial functions)

hi,

I've been looking everywhere to find an answer to this question, Basically, an equation is given

F(x)=3x(2-x)(x+1)(3+x)

What is the total local max and minimum value?

Please help me, my head is about to explode!! thank you!!

I've never heard of the "total max" of a function. (I've heard of absolute and local maximums, though.) How does your book define this term?

Thank you!

this is how my book defines it

local maximum -the point on a function that has the greatest y value on some interval close too the point
local minimum -the point on a function that has the least y value on some interval close too the point

I dont need to know the exact value but how many (i.e. 3 local min/max values or 2 local min/max) max and min!

sorry! my question shoould be how many local max/minimum

I can't imagine why you'd be expected to find exact local max/min points from the graph...? Have you studied any calculus at all?

Originally Posted by stapel

I can't imagine why you'd be expected to find exact local max/min points from the graph...? Have you studied any calculus at all?

Nevermind I think I found the answer.
I think my question was unclear, im gonna try to clarify it. What Im trying to ask is how many local maximum or minimum (not the exact value), is in this function

F(x)=3x(2-x)(x+1)(3+x)

without graphing. From what I understand (n-1), where n is the degree of function is equal to the number of local maximum and local minimum. So in my equation the degree is 4, therefore the # of local max and min is 3, (4-1=3), correct answer. I think i got this right, unless someone thinks otherwise. But then I have another question, because i think this (n-1) doesnt apply to all functions. For instance

P(x)= X^6-16X^2+3

the # of local max and min is = 3, i thought it would be 5 (6-1). Please someone explain why its 3, without graphing?