Question

Intermediate Value Theorum

Answer 1

@zepdrix do you think you'll be able to assist me?

Answer 2

So uhh, do you kind of understand the IVT?

Answer 3

We need to do a couple things:

We're given a function h(θ).
We want to check a couple points h(a) and h(b).

If the function gives us a negative value at h(a),
and a positive value at h(b),

then the function had to cross through zero at some point between a and b, yes?
This is assuming that the function is continuous (which we'll also need to determine at the end).

Answer 4

For our a and b, we'll use the end points of our interval.

So let's find values for `h(0)` and `h(π/4)`.

Answer 5

is theta our variable?

Answer 6

Yes.

Answer 7

So plug zero in for theta, and get some kind of answer for h(0).
h(θ) = 1 - 3tanθ


h(0) = 1 - 3tan0 = ?

Answer 8

-1

Answer 9

Hmmm... no.

tan0 = 0

So we should get 1 - 3tan0 = 1 - 0 = 1

Answer 10

sorry i knew it was 1 idk why i put -1, and the second one should be -2 right?

Answer 11

Yes good!
Since our function went from POSITIVE to NEGATIVE over that interval,
it means the function must have crossed through h(θ) = 0 somewhere in that interval.

The only other thing to worry about it is continuity.

Answer 12

Tangent has a discontinuity at pi/2, but we're not going that far.
So we won't have any problems.

Just make sure you make a note near the end that h(θ) is continuous over the entire interval, or something like that.