18 -5 points scalc7 1.8.051 My Notes Ask Your Teacher Use the Intermediate Value

Question

18 -5 points scalc7 1.8.051 My Notes Ask Your Teacher Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. x4 x 4 0, (1, 2) I. Since -2 Y 14 fx) x4 x 4 is Select on the closed interval [1, 21, f(1) and f(2) there is a number cin (1, 2) such that fc) L? v by the Intermediate Value Theorem. Thus, there is a -Select of the equation x4 x 4 0 in the interval (1, 2) Submit Answer Save Progress View Previous Question Question 18 of 20 View Next Question

Explanation / Answer

f(1) = 1^4 + 1 - 4 = 1 + 1 - 4 = -2

f(2) = 2^4 + 2 - 4 = 16 + 2 - 4 = 14

So, answer is :

f(x) = x^4 + x - 4 is "INCREASING" on the closed interval [1 , 2]

f(1) = -2 and f(2) = 14.

Since -2 < 0 < 14,

there is a number c in (1 , 2) such that f(c) = 0

by intermediate value theorem.

Thus, there is a ROOT of the equation x^4 + x - 4 = 0 in the interval (1 , 2).

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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