Use the intermediate value theorem to determine if
h[theta]=1- 3 tan theta
has a zero in the interval [0,pi/4].
Use form IVT to answer

Question

Use the intermediate value theorem to determine if 
h[theta]=1- 3 tan theta
has a zero in the interval [0,pi/4].
Use form IVT to answer

anonymous · Answer

If $h(\theta)$ is continuous over than interval, you should be able to check to signs on the endpoints, then determine if $h$ crosses the $\theta$-axis.

anonymous · Answer

So yes, it is continuous, because the domain of the tangent function is $\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$.

Evaluate the endpoints:
$$h(0)=1-3\tan0=1-0=1\
h\left(\frac{\pi}{4}\right)=1-3\tan\frac{\pi}{4}=1-3=-2$$
Since $h(\theta)$ changes from positive to negative values over the interval, and since it's continuous over this interval, there must be some value $c$ such that $h(c)=0$.