
7-6 Calculus – Differentiation and Integration
Definition 7.2 Extreme Values
Maximum and minimum values of a function are called its extreme values or turning points. So, a
function, f(x), has an extreme value or extremum at x = a, if it has either a minimum or maximum
value at a.
Properties of Maxima and Minima
At least one maximum or one minimum must lie between two equal values of a function. Maximum
and minimum values must occur alternatively.
• A function y = f(x) has a maximum at x = a, if
dy
dx
changes its sign from +ve to -ve as x passes
through a.
• A function y = f(x) has a minimum at x = a, if
dy
dx
changes its sign from -ve to +