SOLUTION: What are the relative minimums and maximums of your coaster with a polynomial of x^5-4x^4-7x^3+14x^2-44x+120

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Question 1129764: What are the relative minimums and maximums of your coaster with a polynomial of x^5-4x^4-7x^3+14x^2-44x+120
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Relative maximums are the highest points of a section of a graph
Relative minimums are the lowest points of a section of a graph


function x%5E5-4x%5E4-7x%5E3%2B14x%5E2-44x%2B120+has local maximum and minimum where first derivative is equal to zero:

and it is 5+x%5E4+-+16+x%5E3+-+21+x%5E2+%2B+28+x+-+44=0 which is:
x=+-1.89
x=4.03

if x=+-1.89
y=%28-1.89%29%5E5-4%28-1.89%29%5E4-7%28-1.89%29%5E3%2B14%28-1.89%29%5E2-44%28-1.89%29%2B120+
y=225.27

Relative maximum: at point (-1.89,225.27)

if x=+-1.89
y=%284.03%29%5E5-4%284.03%29%5E4-7%284.03%29%5E3%2B14%284.03%29%5E2-44%284.03%29%2B120+
y=-280.19

Relative minimum: at point (4.03,-280.19)