# How do you find the slope of a tangent line to the graph of the function #f(x) = 8 sqrt(-3x - 1)# at x=-3?

Simplifying:

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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, to find the slope of the tangent line to the graph of f(x) = 8√(-3x - 1) at x = -3, you need to follow these steps:

- Find the derivative of the function f(x) with respect to x.
- Substitute the value x = -3 into the derivative to find the slope at that point.

Let's calculate the derivative of f(x) = 8√(-3x - 1):

f'(x) = d/dx [8√(-3x - 1)]

Using the chain rule, we have:

f'(x) = 8 * (1/2) * (-3x - 1)^(-1/2) * (-3)

Now, substitute x = -3 into the derivative:

f'(-3) = 8 * (1/2) * (-3(-3) - 1)^(-1/2) * (-3)

Simplifying further:

f'(-3) = 8 * (1/2) * (-8)^(-1/2) * (-3)

Finally, calculate the value:

f'(-3) = -12/√8

Therefore, the slope of the tangent line to the graph of f(x) = 8√(-3x - 1) at x = -3 is -12/√8.

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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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