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Show the curve has no stationary points.

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 :biggrin:

Reply 1

foldingstars45

yeah a curve with no stationary points is possible, it means that nowhere on the curve has a gradient of zero

Reply 2

DeeDub

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

(edited 13 years ago)

Reply 3

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

Reply 4

foldingstars45

I think to show this, you have to differentiate the curve equation - though I could be wrong, I think i second opinion is needed :smile:

Reply 5

EEngWillow

To show that there are no stationary points, you need to show that you can't solve your gradient function.

(edited 13 years ago)

Reply 6

marek35

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