Verify that the function satisfies the conditions of the Mean Value Theorem on t

Question

Verify that the function satisfies the conditions of the Mean Value Theorem on the closed interval. This answer has not been graded yet. Then find all numbers c in (a, b) guaranteed by the Mean Value Theorem. (Enter your answers as a comma-separated list.) Additional Materials a eBook -10.36 points SullivanCalc1 4.3.029 Verify that the function satisfies the conditions of the Mean Value Theorem on the closed interval. on [i, 27] This answer has not been graded yet Then find all numbers cin (a, b) guaranteed by the Mean Value Theorem. (Enter your answers as a comma-separated list.)

Explanation / Answer

The given function f(x) =(x+3)/x= 1 +3/x is continuous in given interval [1,3]. Also it is diffrentiable in the interval (1,3), because only point it is is not defined is x= 0 which is outside the given interval.

Hence using mean value Theorem

f'(c) =f(3) -f(1)/(3-1)

-3/c² = (2-4)/(2)

-3/c² = -1

c² =3

c= sqrt(3)

Use square root symbol in place of sqrt.

=============

The given function f(x) =x^(2/3) is continuous in given interval [1,27]. Also it is diffrentiable in the interval (1,27),

Hence using mean value Theorem

f'(c) =f(27) -f(1)/(27-1)

2/(3*c^(1/3)) = (9-1)/26

c^(1/3) = 13/6

c=(13/6)^3

c= 2197/216

Related Questions

Navigate

• Browse (All)
• Browse V
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.