I always seen the derivative of a function $y=f(x)$,$\frac{dy}{dx}$ at $x_1$ as the slope of the line tangent to the curve $y=f(x)$ drawn at $y=f(x_1)$.But I often fail to appreciate this when $\frac{dy}{dx}=0$ at some point $x_1$ .
Can anyone please tell me the geometrical significance of $\frac{dy}{dx}=0$
or
draw an analogy which would apply to the above-mentioned case?
(In fact, analytically, what is a tangent to a curve?)
Sorry for so many weird questions.I hope I am not being too incoherent.