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The particle's position as a funciton of...

The particle's position as a funciton of time is given as `x=5t^2-9t+3`. Find out the maximum value of position co-ordinate? Also, plot the graph.

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`x=5t^(2)-9t+3`
`(dx)/(dt)=10t-9=0`
`therefore t=9//10=0.9`
Check, whether maxima or minima exists. `(d^(2)x)/(dt^(2))=10gt0`
`therefore` there exists a minima at `t=0.9`
Now, Check for the limiting values.
When `t=0 , x=3`
`t=oo , x=oo`
So, the maximum position co-ordinate does not exist.
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