Geometrical meaning of derivative at a point:

The derivative  of function y = f(x) at point P(x, y) is equal to the slope  of the tangent line to the curve y = f(x) at P(x, y).

Slope of tangent to curve y = f(x) at the point (x, y)  is  m = tanθ =                          

Equation of tangent:

The equation of tangent to curve

 y = f(x) at point P(x₁, y₁) is given by  

Notes:

(i) If dy/dx = 0 then tangent to curve y = f(x) at point (x, y) is parallel to the x axis.

(ii) If then tangent to curve       y = f(x) at the point (x, y) is parallel to y-axis.

(iii) If , then the tangent to curve y = f(x) at the point (x, y) makes an acute angle with the positive x-axis and vice versa.

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