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.

Asked by harshit mehrotra | 16th Mar, 2011, 12:00: AM

Expert Answer:

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.

Answered by  | 16th Mar, 2011, 07:41: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.