Question

f(x)=x^4−3x^3 where is the function increasing and where is it decreasing
B) where is the max and the min points

Answer 1

Where it's increasing - wherever f'(x) is positive. It's decreasing where f'(x) is negative.

Max and min points - where f'(x) = 0

Answer 2

So find f'(x) first, then find where it's equal to zero, then you just have to find if it's positive or negative between those points.

Answer 3

You can check f'(x) to the left and right of the points where f'(x) = 0 (just pick x values slightly left and right of where f' is zero), to get an idea of the graph, like this:



Make sense?

Answer 4

yeah sorry i took long to respond i was trying to work it out

Answer 5

You may also need to check the sign of f''(x) at the points where f'(x) is zero - saddle points aren't max/mins, and this graph has one:

https://www.google.com/search?q=x%5E4-3x%5E3&aq=f&oq=x%5E4-3x%5E3&aqs=chrome.0.57j0l3j62l2.729j0&sourceid=chrome&ie=UTF-8

f''(x) is positive or negative at the max/mins, f'' won't be zero at the max/min.

Answer 6

okay thank you

Answer 7

You're welcome :)