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Find all stationary points of y=(x-2)^4 - Texas Instruments TI-89 Calculator

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There is no points of inflection for this function. See cap images below.

find all stationary points of y=(x-2)^4 - find-all-stationary-points-y-x-2-4-m02nsnsyat35z2c5533lg4di-1-0.jpg

Posted on Dec 20, 2015

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Plot the functions y1=(x-2)^4 and y2=x, then see where they intersect.

Posted on Oct 17, 2013


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Can you find stationary points of this equation ((x-1)^1/3)*((x+2)^2/3))

There is only one stationary point for the function y(x)=((x-1)^(1/3))*((x+2)^(2/3)) and it is pointwith coordinates x=0 and y=-1.5859

At first, first derivation is y'(x)=x/((x-1)^(2/3))*((x+2)^(1/3)) and we obtained that y'(0)=0. Then we can find second derivation of the function and for value x=0 we could concluded that y''(0)>0. In this stationary point it is minimum value of the function.
Finally, at the points x=-2 and x=1 we have so called critical values for this function.
See captured images below

1. Second derivation for y(x)

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3. Enlarged detail of the graph y(x)

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