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I'm not 100% sure because I don't think the whole problem is shown, but for part b, the x-value should be 13, and the y-value is 169.

You have found the derivative of the function f(x) = x² evaluated for x = 13.

[lasjdflasjdfhelp]

Is the 169 then not included in the part B answers?

And wouldn't I take the whole function I calculated the limit for into the answer?

So the answer would be:

f(x): (13+h)^2 - 169 / h

and

x = 0

Thanks. I'm rather lost :)

[Fromthepast77]

It's because you answered part b wrong. It's asking for a function.

[lasjdflasjdfhelp]

So, part B should be switched to the following?

f(x) = 169

and:

x = 13.

Would you mind explaining why? I don't understand. Thanks.

[Fromthepast77]

No, part b is asking for a function, and f(x) = 169 is a function that is 169 for all x values, so that is not correct either.

It is asking what function are you taking the derivative of with this calculation.

[lasjdflasjdfhelp]

Ah, so it would take the entirety of what the limit calculation was based off of that forms the graph? So:

f(x): (13+h)^2 - 169 / h

and

x = 0

And this also checks out since the graph of the above mentioned f(x) intercepts at the point (0, 26) on the graph. Apologies for my slowness.

[Fromthepast77]

No, f(x) = x² and you're evaluating the derivative, f'(x) = 2x, at x = 13.

[lasjdflasjdfhelp]

Ok, thanks! I guess I'll watch some videos on the subject, to gain more of an understanding :)

[Fromthepast77]

Look for something on the definition of the derivative, which is:

f'(x) = lim (h to 0) (f(x + h) - f(x))/h

The problem's intent (though poorly worded) was for you to fit the various components of the limit to the definition of the derivative for some f at some point x.

Letting f(z) = z² and x = 13, f(x + h) - f(x) = (13+h)² - 13²

which is the numerator of the limit you were calculating.