Consider the function f(x) = 2-4x^2 on the interval [ -4 , 8 ]. Find the average or mean slope of the function on this interval

By the Mean Value Theorem, we know there exists a c in the open interval (-4, 8) such that is equal to this mean slope. Find the one c that works for this problem.

Find the average or mean slope of the function on this interval.

The Mean Value Theorem tells us that there exists a c in the open interval
( 1 , 11 ) such that is equal to this mean slope. What is the only c that works.

Consider the function
Find the average slope of this function on the interval ( -3 , 0 ).
By the Mean Value Theorem, we know there exists a c in the open interval
( -3, 0 ) such that is equal to this mean slope.
Find the value of c in the interval which works

Consider the function on the interval [ 3 , 6 ].
Find the average or mean slope of the function on this interval.

By the Mean Value Theorem, we know there exists a c in the open interval
( 3 , 6 ) such that is equal to this mean slope. For this problem,
there is only one c that works. Find it.

Consider the function on the interval [ -5 , 8 ].
Find the average or mean slope of the function on this interval.

By the Mean Value Theorem, we know there exists a c in the open interval
( -5 , 8 ) such that is equal to this mean slope. For this problem,
there are two values of c that work. The smaller one is

Consider the function on the interval [ -4 , 4 ].
Find the average or mean slope of the function on this interval.

By the Mean Value Theorem, we know there exists at least one c in the open interval
( -4 , 4 ) such that is equal to this mean slope.
For this problem, there are two values of c that work. The smaller one is

Consider the function on the interval [ 0 , 4 ].
Verify that this function satisfies the three hypotheses of Rolle's
Theorem on the inverval.
is on [0,4]
is on (0,4)
and .

Then by Rolle's theorem, there exists a c such that c. c=