CBSE Class 12-science Answered

(First Derivative Test)

Let f (x) be a real valued differentiable function. Let a be a point on an interval I such that f '(a) = 0.

(a) a is a local maxima of the function f (x) if

i) f (a) = 0

ii) f(x) changes sign from positive to negative as x increases through a.

That is, f (x) > 0 for x < a and

f (x) < 0 for x > a

(b) a is a point of local minima of the function f (x) if

i) f (a) = 0

ii) f(x) changes sign from negative to positive as x increases through a.

That is, f (x) < 0 for x < a

f (x) > 0 for x > a

Hope this clears the concept.

Regards

Team Topperlearning.