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