1.Consider the function f(x)=2x^34x on the interval [2,2]. 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 (2,2)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________ and the larger one is________

2.Consider the function f(x)=1/x on the interval [2,11]. 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 (2,11) such that f(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.___________

3.Consider the function f(x)=4x+5 on the interval [1,6]. 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 (1,6) such that f(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. __________

4.Consider the function f(x)=23x^2 on the interval [6,8]. Find the average or mean slope of the function on this interval, i.e.

f(8)f(6)/8(6)= __________

By the Mean Value Theorem, we know there exists a c in the open interval (6,8) such that f(c) is equal to this mean slope. For this problem, there is only one c

that works. Find it._____________

5.Find the limit. Use l'Hospital's Rule if appropriate. Use INF to represent positive infinity, NINF for negative infinity, and D for the limit does not exist.

lim 7cosx/1sinx=___________

x(/2)^+

1 (1 point) Consider the function f(x) = I on the interval [2, 11]. 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 (2, 11) such that f ' (c) is equal to this mean slope. For this problem, there is only one C that works. Find it. (1 point) Consider the function f(x) = 4V3: + 5 on the interval [1, 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 (1, 6) such that f ' (c) is equal to this mean slope. For this problem, there is only one c that works. Find it. (1 point) Consider the function f(x) = 2 3x2 on the interval [6, 8]. Find the average or mean slope of the function on this interval, i.e. f(8) f(6) _ 8 (6) ' By the Mean Value Theorem, we know there exists a c in the open interval (6, 8) such that f ' (c) is equal to this mean slope. For this problem, there is only one c that works. Find it. Find the limit. Use I'Hospital's Rule if appropriate. Use INF to represent positive infinity, NINF for negative infinity, and D for the limit does not exist. lim 7 cos x x- (1/2) + 1 - sin x(1 point) Consider the function f(x) = 2x3 4x on the interval [2, 2]. 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 (2, 2) 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 and the larger one is