Question
Wed March 16, 2011 By: Harshit Mehrotra

what do we mean by change of sign from positive to negative or vice versa in maxima and minima in first and second derivative test ?please explain briefly with the help of graphs and examples.

Expert Reply
Wed March 16, 2011
Dear Student,
 
Following is the summary:

(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.

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