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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.

3 Answers 3