Sketch f(x) = x + cos x. Homework Help ✎
Use the Intermediate Value Theorem to show there is a root between −1 and 0.
Let x1 = −1. Use Newton's Method to find x3.
How close is x3 to the actual root of f(x)? Calculate the error.
State the conditions of the Intermediate Value Theorem: 'Since f(x) is continuous on the closed domain [−1, 0]...
Prove the thesis of the IVT: ... and f(−1) < 0 and f(0) > 0, there must be a value c, on −1 < c < 0, such that f(c) = 0.
Check your work: x3 = −0.739
x3 and the actual root should be very close.