Find the slope of the tangent to the curve at the point where x = a

[Kaleb]

Homework Statement

http://img214.imageshack.us/img214/4673/mathproblemnw5.png

Homework Equations

lim x->a\frac{f(a+h)-f(a)}{h}

The Attempt at a Solution

Ive tried so many times to figure this out. I first substituted the equation into the formula above and multiplied by the conjugate and ended up removing h from the numerator and denominator leaving a -1/2\sqrt{a}. As you can see I have already lost credit for the problem and cannot redo it, but I still want to know how to do it. Any tips and help is appreciated.

 

[Defennder]

Um, why can't you just differentiate y directly without using the fundamental definition of the derivative? Why not just apply differentiation rule for powers?

 

[Dick]

I would suggest you try writing that as -1/(2*sqrt(a)). I'm really hoping that's what you meant.

 

[Gib Z]

Um, why can't you just differentiate y directly without using the fundamental definition of the derivative? Why not just apply differentiation rule for powers?

It appears from the question type that it is quite possible the OP's course hasn't encountered the power rule yet. And it's still good to know how to do it both ways anyways =]

Kaleb - You probably just typo-ed, but your posted definition of the derivative is incorrect.

 

[Defennder]

If that is true then that is pretty odd. I thought schools always teach the mechanical aspects of calculus before introducing the fundamentals. I learned it that way.