Question

Find the local Maxima or local Minima of
f(x)= x³-3x

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Answer 1

Step-by-step explanation:

f′(x)=3x2−3

=0

Or 

x2−1=0

Or 

x=±1 .

f′′(x)=6x

Hence f′′(−1)<0 maxima.

f′′(1)>0 ... minima.

Hence f(x) attains the maximum value at x=−1 and a minimum value at x=1

f(−1)=3−1=2.

The maximum value is 2

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Answer 2

Answer:

f (x)=x^3-3x

f'(x)=3x^2-3=0

x=+-1

f"(x)=6x=0

x=0

at x=1 in f''(x)

f"(1)=6greater than 0(minima)

f"(-1)=-6lesser than 0(maxima)

f (1)=-2(maximum)

f (-1)=+2(minimum)