Derivatives and relative max's and min's

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The discussion focuses on finding the relative maximums and minimums of the function f(x) = x^3 - 12x^2 + 15x + 16 using its first derivative. The first derivative calculated is f'(x) = 3x^2 - 24x + 15. While the user initially computed the roots as x = 4 ± √44, the correct roots are x = 4 ± √11. This correction is crucial for accurately determining the relative extrema of the function.

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f(x)=x^3-12x^2+15x+16
Use the first derivative to find relative maximums, minimums, or neither.

I am trying to find x to plug it back into f(x) to get my y value, but I am not sure if I am getting the correct x value. I did the first derivative and got 3x^2-24x+15. I then set it equal to 0 and got x=4+- the square root of 44.
Is this correct or am I getting the wrong x-value?
 
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You have correctly computed $f'$, however the roots of $f'$ are not quite correct. These roots are in fact:

$$x=4\pm\sqrt{11}$$
 

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