Need help for sketching the following:
y= -x^3/6 + x^2/3 - x/6
I did y' and got -3x^2/6 +4x/6 -1/6=0 and when I try to solve for the x intercepts, I can't seem to find them
Also I'm having trouble drawing a y dash table in order to graph it, like what are the steps to doing that and how do I fill it in?
Thanks guys
Hey conic! Derivative looks good, remember that solving for y'=0 isn't solving for x-intercepts, it is solving for
turning points:
We now test their nature. You can use one of the y' tables as you call it, or more conveniently, we can use the second derivative test:
Is this a test you are familiar with? What you suggested is comparing the sign of the derivative either side of the turning point, but there is an easier way. Basically, it is using a concavity test to determine the nature of a stationary point. If it is concave down, it is a maximum, if it is concave down, it is a minimum
Finding the x-intercepts is done by equating the initial expression to 0. Remember, the x intercept is where y=0:
Putting all of that (x-intercepts and turning points) together, you should be able to sketch
something like this Hope that makes sense