Find the points of local maxima or local minima, functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be f (x) = x3 – 3x

Asked by Sakshi | 1 year ago |  73

##### Solution :-

Given, f (x) = x3 – 3x

Differentiate with respect to x then we get,

f’ (x) = 3x2 – 3

Now, f‘(x) =0

3x2 = 3 ⇒ x = ±1

Again differentiate f’(x) = 3x2 – 3

f’’(x)= 6x

f’’(1)= 6 > 0

f’’ (– 1)= – 6 < 0

By second derivative test, x = 1 is a point of local minima and local minimum value of f at

x = 1 is f (1) = 13 – 3 = 1 – 3 = – 2

However, x = – 1 is a point of local maxima and local maxima value of f at

x = – 1 is

f (– 1) = (– 1)3 – 3(– 1)

= – 1 + 3

= 2

Hence, the value of minima is – 2 and maxima is 2.

Answered by Aaryan | 1 year ago

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