f(x)=x^3 - 9x^2 +15x + 3
First you find the derivative which is: f'(x)=3x^2-18x+15
Then you use can use then quadratic formula or use that other method, but I'd preferably use the quadratic formula.
-b?√b^2-(4ac)/2a → -(-18)?√(-18)^2-(4*3*15)/2*3 → (18?√324-180)/6 → (18?√324-180)/6 → (18?√144)/6 → (18?12)/6
and then solve by subtracting and adding to get the two x values:
Subtraction: (18-12)/6 → x = 1
Addition: (18+12)/6 → x = 5
And then plug them into the original equation to get y or f(x):
f(x)=x^3 - 9x^2 +15x + 3 → f(1)=(1)^3-9(1)^2+15(1)+3 → f(1) = 10.
f(x)=x^3 - 9x^2 +15x + 3 → f(5)=(5)^3-9(5)^2+15(5)+3 → f(5) = -22.
∴ your coordinates are (1,10) and (5,-22).
(1,10) = Maximum.
(5, -22) = Minimum.
Yay, Calculus. xD