# Consider the function #f(x) = absx# on the interval [-4, 6], how do you find the average or mean slope of the function on this interval?

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To find the average or mean slope of the function ( f(x) = |x| ) on the interval ([-4, 6]), we use the formula for the average rate of change or slope:

[ \text{Average Slope} = \frac{f(b) - f(a)}{b - a} ]

Where ( f(a) ) and ( f(b) ) are the function values at the endpoints of the interval ([-4, 6]), and ( a ) and ( b ) are the corresponding ( x )-values.

First, we find the function values at the endpoints:

[ f(-4) = |-4| = 4 ] [ f(6) = |6| = 6 ]

Then, we calculate the difference in function values and the difference in ( x )-values:

[ f(6) - f(-4) = 6 - 4 = 2 ] [ 6 - (-4) = 6 + 4 = 10 ]

Finally, we plug these values into the formula:

[ \text{Average Slope} = \frac{f(6) - f(-4)}{6 - (-4)} = \frac{2}{10} = 0.2 ]

Therefore, the average or mean slope of the function ( f(x) = |x| ) on the interval ([-4, 6]) is ( 0.2 ).

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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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