Derivative of a sum of functions, also cubic graph roots

[James...]

Derivative of a sum of functions

What would you interperate this as?

It is one of the subsections of Differentiation from the syllabus of a University entrance Exam in November but I cannot think what it is referring to.

Differentiation: Derivative of x^a, including for fractional exponents.
Derivative of a sum of functions. Tangents and normals to graphs. Turning
points. Second order derivatives. Maxima and minima. Increasing and
decreasing functions.

That is the whole section, also, what is a second order derivative? I have done both before as it is based on my first year in college which I have already done but I have never heard them referred to as that before so I am a bit unsure.

Also, I know when I have a quadratic equation, I can find how many real roots it has, but how would I go about finding this if the graph was a cubic as I cannot use the quadratic equation?

Thanks a lot

James

 

[tiny-tim]

Hi James!

Differentiation: Derivative of x^a, including for fractional exponents.
Derivative of a sum of functions …

The syllabus starts by defining derivatives of x, x², x³, and so on, and then shows how to find th derivative of a sum like ax² + bx + c.

… also, what is a second order derivative?

The derivative of a derivative (eg d²y/dx²) … this is relevant to finding turning points.

Also, I know when I have a quadratic equation, I can find how many real roots it has, but how would I go about finding this if the graph was a cubic as I cannot use the quadratic equation?

mmm … wait and find out!

 

[James...]

Thanks a lot for that, didn't realize that was it, glad they are something easy & not hard.

I will do a bit of digging on the cubic then and try to work it out ;)