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Draw the graph of y=x^(2//5)...

Draw the graph of `y=x^(2//5)`

Text Solution

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Domain of the function is R.
`f(0)=0`
Also `f(x) ge0` for all `x inR`.
`f^(')(x) = 2/(5x^(3/5))`
`f^(')(x) gt 0` for `x gt0`, where `f(x)` increases and `f^(')(x) lt 0` for `x lt 0`, where `f(x)` decreases.
Also `f^(')(x)` does not exist at `x=0`
At `x=0, f(x)` is non- differentiable as `y=f(x)` has a vertical tangent here.
`f^('')(x)=-6/(25x^(8/5)) lt 0`
Thus, the graph is always concave downward.
The graph of the function is as shown in the following figure.
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