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Consider the function #f(x) = sqrtx# on the interval [0, 4], how do you find the average or mean slope of the function on this interval?

Answer 1

Samantha Adkison

1/2

Mean slope in an interval ( a, b)

#= (int y'dx)#/(length of the interval)

#=(int dy)/(b-a)#

#=(y(b)-y(a))/(b-a)#. And here, it is

#sqrt4/4=1/2#.

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Answer 2

Axel Alvarez

To find the average or mean slope of the function ( f(x) = \sqrt{x} ) on the interval ([0, 4]), you can use the formula for average rate of change, which is:

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

where ( a ) and ( b ) are the endpoints of the interval.

In this case, ( a = 0 ) and ( b = 4 ).

So, the average slope of the function on the interval ([0, 4]) is:

[ \text{Average Slope} = \frac{\sqrt{4} - \sqrt{0}}{4 - 0} ]

[ \text{Average Slope} = \frac{2 - 0}{4} ]

[ \text{Average Slope} = \frac{1}{2} ]

Therefore, the average or mean slope of the function on the interval ([0, 4]) is ( \frac{1}{2} ).

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Answer from HIX Tutor

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.