nsider the following. -2x5 + 9x4-7x³ - 12x = 0, [3,4] ) Explain how we know that the given equation must have a solution in the given interval. Let f(x) = -2x5 + 9x4-7x3-12x. The polynomial f is continuous on [3, 4], f(3) =18 f(c) = 0 > 0, and f(4) = -240 ✓ . In other words, the equation -2x5 + 9x4-7x³- 12x = 0 has a solution in [3, 4]. >) Use Newton's method to approximate the solution correct to six decimal places. x = x < 0, so by the Intermediate Value Theorem, there is a number c in (3, 4)
nsider the following. -2x5 + 9x4-7x³ - 12x = 0, [3,4] ) Explain how we know that the given equation must have a solution in the given interval. Let f(x) = -2x5 + 9x4-7x3-12x. The polynomial f is continuous on [3, 4], f(3) =18 f(c) = 0 > 0, and f(4) = -240 ✓ . In other words, the equation -2x5 + 9x4-7x³- 12x = 0 has a solution in [3, 4]. >) Use Newton's method to approximate the solution correct to six decimal places. x = x < 0, so by the Intermediate Value Theorem, there is a number c in (3, 4)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Consider the following.
-2x5+ 9x4-7x3 - 12x = 0, [3, 4]
(a) Explain how we know that the given equation must have a solution in the given interval.
Let f(x) = -2x5 + 9x47x3 - 12x. The polynomial f is continuous on [3, 4], f(3) = 18
f(c) = 0
(b) Use Newton's method to approximate the solution correct to six decimal places.
X
X =
> 0, and f(4) =
In other words, the equation -2x5 + 9x47x³- 12x = 0 has a solution in [3, 4].
-240
< 0, so by the Intermediate Value Theorem, there is a number c in (3, 4) such that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c35614e-f53f-486b-9e87-afb8487cbd26%2F370de188-f808-4879-9523-d306f7cbd055%2Ft5jq0i8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following.
-2x5+ 9x4-7x3 - 12x = 0, [3, 4]
(a) Explain how we know that the given equation must have a solution in the given interval.
Let f(x) = -2x5 + 9x47x3 - 12x. The polynomial f is continuous on [3, 4], f(3) = 18
f(c) = 0
(b) Use Newton's method to approximate the solution correct to six decimal places.
X
X =
> 0, and f(4) =
In other words, the equation -2x5 + 9x47x³- 12x = 0 has a solution in [3, 4].
-240
< 0, so by the Intermediate Value Theorem, there is a number c in (3, 4) such that
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