Question

Please explain and show me how to do this step by step? :)

Thank you!!

Show that cos x =x has a solution on the interval [0, π/2].

:)

Answer 1

use intermediate value theorem

Answer 2

f(x) : cosx - x

Answer 3

start with
\[\cos(x)-x\] and then.. what @ganeshie8 said

Answer 4

so f(0) = 1 ? :/

and then also plug in for f(π/2) ?

Answer 5

yes find f(0) and f(pi/2)

if u get opposite signs for them, then it is guaranteed that the function crosses 0 at some point in between - guaranteeing a solution in the given interval

Answer 6

okay:)

so would f(0)=1 and f(pi/2)=-pi/2 ?:/

Answer 7

yahh.. so u got f(0) = positive
f(pi/2) = negative

Answer 8

by IVT, it crosses at 0 at some point in between. QED.

Answer 9

ohh so would it be that there is a solution on the interval [0, pi/2] because through IVT, it crosses 0 at some point?

and the graph shows proof right?

also, not quite sure, but what do you mean by QED?

Answer 10

your statements are 100% correct

QED means end of proof :)

Answer 11

haha okay woo! thank you :)

and ohh i see :) haha thanks for telling me that too :p

:)

Answer 12

would those be the correct labels?