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Functions

A photo of Valentini Valentini
Do any mathematical geniuses have an idea of what I should do in order to find the maximum of this function?

t(x)=-2(x-3)^4+1

I know that the graph includes the points (-1, -17) (1,-2) (3,-1) (5,-2) and (7, -17)

I also know that -1 won't be the maximum y value, however, I'm not sure how to find what the max. y-value would be.

Does anyone have a suggestion of how to solve this?
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A photo of phylloconcrete phylloconcrete

@Valentini wrote
Do any mathematical geniuses have an idea of what I should do in order to find the maximum of this function?

t(x)=-2(x-3)^4+1

I know that the graph includes the points (-1, -17) (1,-2) (3,-1) (5,-2) and (7, -17)

I also know that -1 won't be the maximum y value, however, I'm not sure how to find what the max. y-value would be.

Does anyone have a suggestion of how to solve this?



I can't remember at all how you would do this in just functions, but you can take the derivative then solve for the critical numbers

t`(x)=-8(x-3)^3
for C.N., t'=0
x=3
so the local maximum occurs at (3,1)
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A photo of immaculatedx immaculatedx
he doesn't know any derivatives, it's 11U functions.

Simplest way is you know the vertex of the quartic function is (3,1) so you can test if its a minima or maxima by checking the function value left of 3 and right of 3. you'll notice they're all less than 1 so (3,1) is the maxima.
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A photo of rt7 rt7
u can note that -2(x-3)^4 <= 0. and the max is when it's zero, which is when x=3. and when x=3, y=1. there's your max.
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