# How do you find the slope of a tangent line to the graph of the function #g(x) = 14 − x^2# at (2, 10)?

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Part 2 of 2

Using FIRST PRINCIPLES with explanation about determining the slope

Suppose we have two points on the graph.

This you should have seen before!

In Calculus you start to bring the two points so close together that you can not physically measure the gap between them.

Then the progression point gives us:

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Part 1 of 2

Using shortcut:

Given point

Set

If we have

The constant of

So in this case:

The slop

In other words it is the UNIT RATE OF CHANGE.

So at

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To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function. In this case, the function is g(x) = 14 − x^2. To find the slope at the point (2, 10), we need to find the derivative of g(x) and evaluate it at x = 2. The derivative of g(x) is given by g'(x) = -2x. Evaluating this at x = 2, we get g'(2) = -2(2) = -4. Therefore, the slope of the tangent line to the graph of g(x) = 14 − x^2 at (2, 10) is -4.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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