Which one of the following is correct in respect of the function f x x x minus 1 x 1 ........

Mathematics (NDA) Diffrentiation

Which one of the following is correct in respect of the function f(x) = x(x − 1)(x + 1)?

The local maximum value is larger than local minimum value.

The local maximum value is smaller than local minimum value.

The function has no local maximum.

The function has no local minimum.

f’(x) = 3x² - 1

f’’(x) = 6 x

Put f’(x) = 0 implies that x = ± 1 / √3

Putting in f’’(x): Maxima will be at −1 / √3 and minima will be at 1 / √3

∴ Max f(x) = f(−1 / √3 ) = 2 / 3√3

Min f(x) = f( 1 / √3 ) = −2 / 3√3

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