Derivatives in my calculus class

[Haroldoo]

I am on my second day of derivatives in my calculus class (I am taking it over the summer) and I was wondering if there is a check that you can preform to see if your answer is correct?
I do some questions and I think I got it right but I am just never sure if I have made an arithmatic error or somthing, somewhere.

 

[Hurkyl]

You could do the problem twice, see if you get the same answer. Similarly, you could try to do the same problem in multiple ways.

You could graph the function and see if it is increasing only where the derivative is positive. You could use the derivative to compute some tangent lines, and see if the tangent line really is tangent to the graph.

The derivative is a limit -- you could try plugging in a value that is near the limiting point, to see if you get something nearly equal to the derivative.

 

[nicktacik]

Sure, here's a trick. Suppose you evaluate the derivative of f(x) at x0 to be L. Try evaluating [f(x0+0.0001]-f(x0)]/0.0001 with your calculator. You should get approximately L.

 

[Gza]

Try integrating the answer and seing if you come up with the original function

 

[Gib Z]

Try integrating the answer and seeing if you come up with the original function

He's on his third day on differentiation, I don't think indefinite integration is quite within his reach yet.

 

[ice109]

He's on his third day on differentiation, I don't think indefinite integration is quite within his reach yet.

sure it is considering the indefinite integral is just the antiderivative

 

[Gib Z]

>.< Well I'm not sure he's learned the Fundamental Theorem of Calculus either ! :P