Question

Use the Intermediate Value Theorem to determine if h(x)= 1-3tanx has a zero in the interval [0,pi/4]. You must show how you arrived at your answer using the IVT.

Answer 1

the thing is to find an \(x_1\) and an \(x_2\) such that \(h(x_1)<0\) and \(h(x_2)>0\). Then the theorem tells you that .....

Answer 2

\[
f(x) = 1 - 3 \tan(x) \\
f(0) = ? \\
f(\pi/4) = ?? \]

Answer 3

With the two values f(0) = 1 and f(pi/4)= -2, what's the next step? (-2+1)/2=-.5?

Answer 4

you use immediately the theorem

Answer 5

thanks to the theorem ew know that there's an \(x\) in the interval such that \(f(x)=-1\). but that works for the value 0 too.. (any value between 1 and -2)

Answer 6

ohh ok, thanks.