Differentiation Curve Sketching (1 Viewer)

[atar90plus]

Hello
I want to ask a few questions relating to differentiation curve sketching. In a quadratic equation one of the steps my teacher told me is to find out whether the quadratic is a positive or a negative definite. So what does the positive or negative definite represent differentiation curve sketching?

My second question is what are the steps in solving oblique asymptotes in relation to differentiation curve sketching as well? Also what does it mean to cut oblique asymptotes?

If you guys can show me by an example preferably with a diagram it would be greatly appreciated

Thanks

 

[ismeta]

A definite quadratic means that it does not have real roots, i.e. it does not touch or intersect the x-axis (thus, Δ < 0).

A positive definite means that its concavity is positive (faces upwards) and always has positive y-values. (and f''(x) > 0). A negative definite is where a quadratic's concavity is negative, always has negative y-values and is concave down - f''(x) < 0.


(sorry about the hastily drawn diagram)