Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-

Question

3 years ago

12

separated list. If an answer does not exist, enter DNE.) f(x) = x , [0, 16]

1 answer:

katrin2010 [14] · Answer 1 · 2022-06-04T13:44:10+03:00

Answer:

C = 4

Step-by-step explanation:

solution:

f(x) can be differentiated on (0,16)

By mean value theorem

= f(16) = 4

= f(0) = 0

= f(b) - f(a)/b - a

= f(4) - f(0)/ f(16) - f(0)

= f'(c) = 1/2√C

= 1/2√C = 4/16

= 1/2√C = 1/4

= 4 = 2√C

= √C = 4/2

we make c the subject of the formula and also eliminate the square root

= √C = 2

= C = 2²

= C = 4