Question

1. Determine whether Rolle's Theorem can be applied to f on the closed interval

[a, b].

(Select all that apply.)

f(x) =

x2− 4x − 5

x + 5

,    [−1, 5]

Yes, Rolle's Theorem can be applied.No, because f is not continuous on the closed interval [a, b].No, because f is not differentiable in the open interval (a, b).No, because f(a) ≠ f(b).

If Rolle's Theorem can be applied, find all values of c in the open interval

(a, b)

such that

f '(c) = 0.

(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)

c =

2. The height of an object t seconds after it is dropped from a height of 230 meters is

s(t) = −4.9t² + 230.

(a) Find the average velocity of the object during the first 6 seconds.
m/s

(b) Use the Mean Value Theorem to verify that at some time during the first 6 seconds of fall, the instantaneous velocity equals the average velocity. Find that time.
s

Answer 1

Rolle’s theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

As we can see given function is continuous in interval [-1,5] and also differentiable in interval (-1,5).Also

and

Hence rolle's theorem can be applied here.

now     

now let f'(x)=0 for some . Then

Or

Now solving by sridharachary method , we get