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markosheehan
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is the function x³-5x²+3x+5 injective. how can you tell
MHB Determining if a function is injective
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To determine if the function x³-5x²+3x+5 is injective, one must check for local extrema. A function is not injective if it has a local maximum or minimum, as it will take the same value at different points. Analyzing the derivative can reveal critical points where the function may change direction. If the derivative does not change sign, the function is injective. Thus, examining the behavior of the derivative is essential for establishing injectivity.
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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