Question

For y = x^4 - 72x^2 - 17, how would I find each of these?
a) where the function is increasing
b) where the function is decreasing
c) where the function is concave up
d) where the function is concave down
e) inflection points

Answer 1

are you in algebra I or in calculus?

Answer 2

methods matter

Answer 3

look at the graph

Answer 4

then you need to take the derivative of your function and set it equal to zero and solve it

Answer 5

then you will have to do a sign analysis to see where the funciton is increasing and decreasing

Answer 6

then I would take the second derivative and solve it, this will tell you where the function is concave up or concave down

Answer 7

Find the critical points by setting the first derivative to 0. These points are where the function switches between inc/dec. Like precal said, make a sign diagram with the critical points on it and plug in numbers in between the critical points into the first derivative. If you get a positive value, it's increasing, if you get a negative value, it's decreasing. Same concept for concave up/down but with the second derivative.

Answer 8

first derivatives tell you where the function is increasing or decreasing
second derivatives tell you where the function is concave up or concave down

Answer 9

Here is a video if you have time
http://www.khanacademy.org/math/calculus/differential-calculus/critical_points_graphing/v/maxima-minima-slope-intuition

if this does not make sense, the other videos might help...