MHB Derivatives and relative max's and min's

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The first derivative of the function f(x)=x^3-12x^2+15x+16 is correctly calculated as f'(x)=3x^2-24x+15. Setting the first derivative to zero helps identify critical points for relative maximums and minimums. The correct roots of the first derivative are x=4±√11, not x=4±√44. Evaluating these critical points will help determine the nature of the extrema. Accurate computation of these values is essential for finding the corresponding y-values in f(x).
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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:

$$x=4\pm\sqrt{11}$$
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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