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Consider the function /(z) = = on the interval [4, 7). Find the average or
mean slope of the function on this interval,
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By the Mean Value Theorem, we know there exists a e in the open interval
(4, 7) such that f'(c) is equal to this mean slope. For this problem, there is
only one c that works. Find it.
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If we apply Rolle's Theorem to the function /(x) = 2 - 8x - 4 on the
interval [0, 4], how many values of c exist such that /'(c) = 0?
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What is the value of c?
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If we try to apply Rolle's Thorem to the function /(z) = 2r- 8x - 4 on
the interval [ - 3, 11], which of the following conditions is not met?
. differentiability on [ - 3, 11]
Of(a) # f(b)
O continuty on [ - 3, 11]
Consider the function /(x) = 2x3 - 913 - 24x + 2 on the interval
[ - 6, 10). Find the average or mean slope of the function on this interval.
Preview
By the Mean Value Theorem, we know there exists a e in the open interval
( - 6, 10) such that f'(c) is equal to this mean slope. For this problem, there
are two values of c that work.
The smaller one is
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and the larger one is
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Top Answer

Simple calculations by using... View the full answer

IMG_20200105_160549.jpg

@ {( x) = on [ 497]
The average Rate of change over an interval [a, b] is
given by: 8(b )- fla)
b - a
Now by given [4, 7] ; a = 4 , 6= 7
7
y
-7 =
28
28
" 8(b )- fla) = (#7 )-(4 )
=
-31
b - a...

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