Question

Graph the function f(x) = x4 − 7x3 + 12x2 + 4x − 12 using graphing technology and identify for which values of x the graph is increasing.

Answer 1

You'd graph it: http://www.wolframalpha.com/input/?i=graph+f%28x%29+%3D+x4+%E2%88%92+7x3+%2B+12x2+%2B+4x+%E2%88%92+12

You'd also find for what x values the derivative of f(x) is positive, this can be done by using your graphing calcultor, putting y1= F'(X), and y2=0, find the intersection points between the two equations.
Although you can tell by simply staring at the graph which of the parts are positive, and which aren't, you could justify it with a Sine Chart, by plotting all interception points(where f'(x) = 0), and testing intermediate values for positive or negativity.

Answer 2

f'(x) = 4 x^3-21 x^2+24 x+4

Answer 3

but idk how to determine the values that increase on the graph

Answer 4

It's increasing from the interval of -.14718 to 2.
http://www.wolframalpha.com/input/?i=Zereos+of++f%28x%29+%3D+4+x%5E3-21+x%5E2%2B24+x%2B4

Answer 5

ok thank you!