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Why is it so that in the velocity time graph, even though the derivative of the function at a point x is zero, the velocity is said to be maximum:
enter image description here

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    I guess the horizontal axis is time and vertical one is the space. But what is x, is it time or space? – 2017-02-24
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    Who says "the velocity is maximum" there? As you suspect, the velocity is $0$. The height is a maximum. The velocity might be at a maximum when the second derivative is $0$. – 2017-02-24
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    At the maximum, the vehicle returns. To do so it must invert its speed, i.e. let it pass through zero. – 2017-02-24
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    @Ilis, yes, the horizontal axis represents time and the vertical represents the function of time as velocity – 2017-02-25

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if we take the function $v(t)=s'(t)$ describing the velocity, then $v'(t)=s''(t)$ describes the acceleration and $v'(t)=0$ means (of course if $\exists \delta>0 \forall \epsilon<\delta\,: v'(t-\epsilon)\cdot v'(t+\epsilon)\leq 0$), that the velocity reaches the local extremum (maximum or minimum).

On the other hand, If we have a function $s(t)$ describing dependence of distance and time, then $s'(t)$ describes the velocity. $s'(t) =0$ means then, that the velocity is equal to $0$, not maximum. This is for the distance time graph.

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    did some error above, and tried to fix it – 2017-02-25