Homework SourseConsider the equation x3 x 4 0 Use the Intermediate Value
Consider the equation x3 + x ? 4 = 0.
Use the Intermediate Value Theorem to show that there is a root of this
equation in the interval (1, 2) by checking all the criterions in IVT.
Use a graphing calculator to ?nd an interval of length 0.01 that contains
this root.
Use the Intermediate Value Theorem to show that there is a root of this
equation in the interval (1, 2) by checking all the criterions in IVT.
Use a graphing calculator to ?nd an interval of length 0.01 that contains
this root.
Solution
f(x) = x^3 + x - 4
f(1) = 1+1-4 = -2
f(2) = 8+2-4 = 6
f(1)f(2) < 0
and f(x) is continuous
-> by intermediate value theorem, f(x) has a root between 1 and 2.
Using calculator:
root 1.3788
0.01 interval: (1.37 , 1.38)
