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# Find the points of local maxima or local minima and corresponding local maximum and local minimum values of each of the following functions. Also, find the points of inflection, if any:

Answer :

f(x) = x

f’(x) =

f’’(x) =

For maxima and minima,

f'(x) = 0

X = ±1

Now

f’’(1) < 0

x = 1 is point of local maxima

f’’(– 1) > 0

x = – 1 is point of minima

hence

local max value = f(1) = 1

local min value = f(– 1) = – 1

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