You take the derivative of the function, set it equal to zero, and solve.
#4
reza
26
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usually we take derivative of function and set it equal to 0 like hage567 said
for example you consider this function
y=x.x+x=x(2)+x
y'=dy/dx
y'=2x+1
for finding the critical number we set it to zero
y'=0
=> 2x+1=0
=> 2x=-1
=> x=-1/2
-1/2 is critical number for this function
and one of its usage is for finding the MAX. and MIN. of a function.
No. Critical points are where either the derivative is 0 or where the derivative does not exist. Points of inflection are where the secondderivative changes sign. That has to be where the second derivative is 0 or does not exist although not all such points are inflection points.
For example, if f(x)= x3- 3x, then df/dx= 3x2- 3 so the critical points are x= 1 while d2f/dx2= 6x. The only inflection point is at x= 0.
Hi everybody
If we have not any answers for critical points after first partial derivatives equal to zero, how can we continue to find local MAX, local MIN and Saddle point?. For example: Suppose we have below equations for first partial derivatives:
∂ƒ/∂x = y + 5 , ∂ƒ/∂y = 2z , ∂ƒ/∂z = y
As you can see, for ∇ƒ= 0 , there are not any answers (undefined)