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1. The problem statement, all variables and given/known data

-you have the curve [tex]y = 2x^2 - 4x + 2[/tex]

-find its intersections with y and x axis, call them A and B.

-in the parabolic sector limited by these two points, find a point P, in the way that the sum of its cohordinates is minimum and maximum.

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results:

P cohordinates for minimum sum are (3/4 ; 1/8),

for max sum:(0 ; 2)

2. Relevant equations

3. The attempt at a solution

the general cohordinates of P are P(x ; 2x²-4x+2), so i set the function:

y=x+2x²-4x+2 and calculate where it has min or maximums, with the condition of [tex]0 \leq x \leq 1[/tex].

so y'=4x-3: 4x-3 > 0, x > 3/4. now i should put in the disequation the condition [tex]0 \leq x \leq 1[/tex] right? but it goes wrong.

it gives me a maximum in x=0, ok, a minimum in x=3/4, ok, and another maximum in x=1, not ok.

for me it's the first attempt to those problems please tell me where i'm wrong.

(i didn't put cohordinates as absolute values because i saw that in that "x" interval they are ok as i put them).

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# Problem with max and min, i found half solution, need the other half

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