Using definition of derivative

[Euler]

A problem in my book requires me to use the definition of derivative

(The first listed one, which has delta x —> 0.)

I was able to complete the first one of these, and got the answer right (comparing it by taking the power rule of the original equation and seeing if they match up).

This problem however, is not working out for me. I don't know how exactly to plug the numbers into the equation.

The formula reads 10x²-5x+7.

What should my formula look like when I plug it into the aforementioned definition of derivative? I know the derivative is 20x-5.

 

[tkhunny]

The formula reads 10x²-5x+7.

It should be just algebra for a mere polynomial. Let's see your work on it. Plug it in the top formula, expand the mess in the numerator and, with any luck, stuff will disappear making the limit a bit more tractable for you.

 

[stapel]

I'm going to guess that the exercise is something along these lines:

. . . . .Find the derivative of f(x) = 10x² - 5x + 7
. . . . .from the definition.

However, I'm not clear on whether you are supposed to be finding the general derivative (from the first formula) or the derivative at some point c (from the second formula).

Please reply with clarification. The full and exact text of the exercise and instructions would be very helpful. Thank you.

Eliz.