Question

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval: x^4+x-3=0, (1,2)

Answer 1

Ok the interval is (1,2) so they are looking for you to use the Int Value Thm.... Do you know what this theorem means?

Answer 2

Try and explain it to me and I will see if you nail it.... formulas are important but understanding is more so

Answer 3

Ok well my teacher gave me the theorem and said if f is continuous on an interval and N is any number between f(a) and f(b) then there exists C on (a,b) such that f(c)=N. Not sure I understand that though....

Answer 4

Ok let discuss then.... the easiest way is to think in terms of what happens when you use it to find a zero of a polynomial... like your problem for instance

Answer 5

Since f is continuous there are no holes, jumps, gaps, kinks, etc.... so it can be represented by a smooth curve

Answer 6

now lets take the interval from (a,b) and stipulate that f(a) is positive and f(b) is negative (i.e. f(a)>0 and f(b)<0)

Answer 7

Since f is continuous the graph of the function must have crossed the x-axis somewhere inside the interval in order for the value of the function to change signs