Determine if the function f(x)=44−x2√ satisfies the mean value theorem on [0, 2]. if so, find all numbers c on the interval that satisfy the theorem.

The function f(x) satisfies the Mean Value Theorem

Step-by-step explanation:

Mean Value Theorem states that if f be a function such that,

Then there is at least a number c in (a, b) such that,

Here, the given function,

∵ f(x) is defined for all real values x for which 44-x² ≥ 0

44 ≥ x² ⇒ ±√44 ≥ x ⇒-√44 ≤ x ≤ √44

Thus, f(x) is continuous on [0, 2],

∵ f'(x) is defined for all values on the interval (0, 2),

Thus, f(x) is differentiable on (0, 2),

Now,

Hence, the function f(x) satisfies the Mean Value Theorem

c

step-by-step explanation:

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.