Question

show steps.

For f(x)=(x^3)-90x^2,

a. find the intervals where f(x) is increasing and decreasing.







b. find the intervals where f(x) is concave up and concave down.







c. find where f(x) has a relative max and relative min.






d. find where f(x) has an inflection point.





e. find the x and y intercepts of y=f(x) .





f. sketch the graph of y=f(x) .






g. find the absolute minimum and absolute maximum of f(x) on the interval [-1,1].
show steps.

For f(x)=(x^3)-90x^2,

a. find the intervals where f(x) is increasing and decreasing.







b. find the intervals where f(x) is concave up and concave down.







c. find where f(x) has a relative max and relative min.






d. find where f(x) has an inflection point.





e. find the x and y intercepts of y=f(x) .





f. sketch the graph of y=f(x) .






g. find the absolute minimum and absolute maximum of f(x) on the interval [-1,1].
@Mathematics

Answer 1

f(x)=(x^3)-90x^2

First, let's take the derivative and discover the critical points, or the maxes and mins.

0=3x^2-180x
3x^2=180x
x^2=60x
x=60 or x=0
Zero is a maximum, and 60 is a minimum.
Therefore the function is increasing from negative infinity to zero, decreasing from zero to sixty, and increasing from 60 to infinity.

That should get you started on the rest of the problem!

Answer 2

how do i do g? thanks so much btw.