Q. 3 A 3.7( 16 Votes )

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:

f (x) = x2

Answer :

f(x) = x2

f’(x) = 2x

Now, f’(x) = 0

x = 0

x = 0 is the only critical point which could possibly be the point of local maxima or local minima of f.

f’’(0) = 2, which is positive.

Then, by second derivative test,

x = 0 is point of local maxima and local minima of f at x = 0 is f(0) = 0.

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RS Aggarwal - Mathematics