# Calculus

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A function has a relative Maximum of (0,0) and a relative minimum of (3,-5). What is the function?

• Calculus -

assuming a polynomial, we see that y' is a quadratic, so

y = ax^3 + bx^2 + cx + d
(0,0) => d=0
(3,-5) => 27a+9b+3c=-5

y' = 3ax^2 + 2bx+c
y'(0) = 0 => c=0
y'(3)=0 => 27a+6b=0

solving for a and b, we get

y = 10/27 x^3 - 5/3 x^2

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