Application of derivatives

Tangent and Normal

Slope of tangent = dy/dx

Slope of normal = - 1/(dy/dx)

Angle between two curves = tan-1[(m1m2)/1m1.m2)]

Length of tangent = y1(√(1+1/m2))

Length of sub-tangent = y1/m

Length of normal = y1(√(1+m2))

Length of sub-normal = y1.m

Extreme value theorem

If f is continuous in [a , b], then f has both a maxima and a minima in that interval.

Rolle’s Theorem

If f is continuous on [a , b] and is differentiable in (a , b) and if f(a) = f(b), then there is atleast one c