For what values ofxis the graph ofy=x4 - 9xboth increasing and concave up?.....

how do i figure this out? i graphed the function, and see where it is concave up, but dont know how to tell what the values are...any help?

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- September 24th 2007, 09:29 PMmer1988a bit of concavity
For what values of

*x*is the graph of*y*=*x*4 - 9*x*both increasing and concave up?.....

how do i figure this out? i graphed the function, and see where it is concave up, but dont know how to tell what the values are...any help? - September 24th 2007, 09:30 PMJhevon
- September 24th 2007, 09:47 PMmer1988
yes i know that, but how do i find out the x values?

- September 24th 2007, 10:33 PMticbol
y = x^4 -9x

y' = 4x^3 -9

y'' = 12x^2

y' determines the slope of the curve. If y' is negative, the graph is going down. If y' is positive, the graph is going up. If y' = 0, the graph is horizontal, neither decreasing nor increasing. So, y' > 0 if graph is increasing.

y' = 4x^3 -9

4x^3 -9 > 0

x^3 > 9/4

x > cubrt(2.25) -----the graph is increasing.

y'' determines the concavity of the curve.

If the y'' is positive, then the concavity of the graph is facing upwards.

y'' = 12x^2

Except for x=0, for any real values of x, the y'' is positive.

Therefore, for the graph of y = x^4 -9x is increasing and concaves up for all values of x, such that x > cubrt(2.25). -----------answer.