# How do you find the slope of the secant lines of # f(x) = x^2 + 5x# at (6 , f(6)) and (6 + h , f(6 + h))?

Slope

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To find the slope of the secant line between the points ((6, f(6))) and ((6 + h, f(6 + h))) on the function (f(x) = x^2 + 5x), we first need to find the corresponding function values at these points.

(f(6) = (6)^2 + 5(6) = 36 + 30 = 66)

(f(6 + h) = (6 + h)^2 + 5(6 + h) = 36 + 12h + h^2 + 30 + 5h = h^2 + 17h + 36)

Now, we can use the formula for the slope of a secant line:

[ \text{Slope} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{f(6 + h) - f(6)}{(6 + h) - 6} ]

[ = \frac{(h^2 + 17h + 36) - 66}{h} ]

[ = \frac{h^2 + 17h - 30}{h} ]

This expression represents the slope of the secant line between the two given points on the function (f(x) = x^2 + 5x).

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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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