MAXIMA AND MINIMA - created from Mind Map

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MAXIMA

LOCAL MAXIMA AND MINIMA

FIRST DERIVATIVE TEST FOR LOCAL MAXIMA AND MINIMA

FIRST DERIVATIVE TEST FOR LOCAL MAXIMA AND MNIMA

Let f(x) be a real function defined on an interval [a ,b].

then there exist a point c in [a,b] such that f(x)<f(c) for all x[a,b]

MINIMA

then there exist a point c in [a,b] such that f(x)>f(c) for all x[a,b]

LOCAL MAXIMA

Put y=f(x)

find dy/dx

Put dy/dx=0 and solve this equation for x .let C1, C2, C3,.......Cn be the roots of the this equation . these points (stationary values of x ) are possible points where

Put y=f(x) and find dy/dx

Put dy/dx=0 and solve

Consider x=C1

If dy/dx changes its sign from + to - as x increases through c1 then fuction attains a local maximum at x=C1

If dy/dx changes its sign from - to + as x increases through c1 then fuction attains a local minimum at x=C1

If dy/dx does not change its sign as x increases through c1 then x=C1 is neither a maximum nor a point of local minimum .This point is called POINT OF INFLEXION

Continu this for other values of x