Answer to Question #88314 in Math for Shivam Nishad

Question #88314
Find the values of x for which the function f(x)=x^3–3x, is increasing.
1
Expert's answer
2019-04-22T13:19:03-0400

Solution. Find the first derivative of the function and find the values when the derivative is zero.


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

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

"x^2=1"

The roots of the equation are


"x_1=-1""x_2=1"

Find the value of the derivative for each of the intervals.

For


"x\\in (-\\infty, -1)"

"f'(x)>0"

function f(x) is increases.

For


"x\\in (-1,1)"

"f'(x)<0"

function f(x) is decreases.

For


"x\\in (1,\\infty)"

"f'(x)>0"

function f(x) increases. Therefore the values of x for which the function f(x)=x^3–3x, is increasing


"x\\in(-\\infty,-1)\\bigcup(1,\\infty)"

Answer. 

"x\\in(-\\infty,-1)\\bigcup(1,\\infty)"


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