Question

Consider the function

?(?)=?^3 − 4x^2 + 3? − 2

1) Find the average slope of this function on the interval (1,5).

2) Find c.

By the Mean Value Theorem, we know there exists a c in the open
interval (1,5)such that f′(c) is equal to this mean slope. Find the
value of c in the interval which works.

I assume the answer of first one is 10, but I wasn't sure how to
approach the second one. Please help!

Answer #1

(1)

The average slope of this function

(2)

From Mean value theorem

Value which is in the given interval (0,5)

f(x)=2x^3−15x^2−36x+8
on the interval [−5,7]. Find the average or mean slope of the
function on this interval.
Average slope = 12
By the Mean Value Theorem, we know there exists at least one cc
in the open interval (−5,7) such that f′(c) is equal to this mean
slope. Find all values of cc that work and list them (separated by
commas) in the box below.
List of numbers:
need answer for second part..

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(x, y) =
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(x, y) =
(smaller x-value)
(x, y) =
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1.) Given the continuous function ?-4x in the
interval [0,1], determine the Fourier coefficients
??,?1,?2,?3.
2.) Reconstruct an approximation to ?-4x by using the
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(a, b) then enter 'a,b' (without the quotes) into the answer box.
(b) Using your critical point in (a), find the value of D(a, b)
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(c) Fill out the sign chart for the derivative below. Please
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