Use the Intermediate Value Theorem to verify that f(x) has a zero in the given interval. Then use the method of bisections to find an interval of length 1/32 that contains the zero.

Question

Use the Intermediate Value Theorem to verify that f(x) has a zero in the given interval.  Then use the method of bisections to find an interval of length 1/32 that contains the zero.

anonymous · Answer

f(x) = x^2 - 7, [2,3]

anonymous · Answer

can u help with this last one then i'm done for today @zepdrix

zepdrix · Answer

Well we can determine where f(x) has a zero by setting the function equal to zero and solving for x.$$\large f(x)=x^2-7 \qquad \rightarrow \qquad 0=x^2-7 \qquad \rightarrow \qquad x=\sqrt 7$$
$\sqrt 7$ is approximately $2.65$ which is between 2 and 3.

I'm not exactly sure how to apply the Intermediate Value Theorem, or Bisections for that matter :( Hmmm
But that's where the root is located at least :C

anonymous · Answer

okay thanks for the help i appreciate it