Question

find the local maximum value of the function g(x)=x^3-3x​

Answer 1

Answer:

B

local max. at x=−1, local min. at x=1

f

′

(x)=3x

2

−3

=0

Or

x

2

−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

Answer 2

Step-by-step explanation:

f(x) = 3x^2-3

=0

or

x^2-1=0

or

x=±1

f(x) =6x

hence f(-1) ≤0 Maxima

f(1) ≥ 0 minima

hence f(x) attains maximum value at x = -1 and a maximum value at x = 1

f(-1) =3-1=2

the maximum value is 2