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# Show the curve has no stationary points. watch

1. Q. Hence show that the curve with the equation: y=(2+x)^3 - (2-x)^3
has no stationary points. (the questions prior to this were binomial expansion of the above cubics)

I simplified y to y=2x^3 +24x. This could be wrong though.
Is it possible to have a curve with no stationary points???

Thanks
2. yeah a curve with no stationary points is possible, it means that nowhere on the curve has a gradient of zero
3. As the indices are 3 then the curve could have a point of inflection but not actually a stationary point. i.e. the second derivative is zero but not the first.

http://www.wolframalpha.com/input/?i=y%3D2x^3+%2B24x
4. yes

differentiate

you get dy/dx = 6x^2 + 24

put it to zero = 6x^2 + 24 = 0
6x^2 = -24
x^2=-4 --> No Solutions

Hope this is right, a long time since I touched this
5. I think to show this, you have to differentiate the curve equation - though I could be wrong, I think i second opinion is needed
6. To show that there are no stationary points, you need to show that you can't solve your gradient function.
7. (Original post by okapobcfc08)
yes

differentiate

you get dy/dx = 6x^2 + 24

put it to zero = 6x^2 + 24 = 0
6x^2 = -24
x^2=-4 --> No Solutions

Hope this is right, a long time since I touched this
yeah thats right, since to find stationary points you need to do dy/dx=0 anyway .

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