Intermediate value theorem
Prove x(x-6)^2=6 has a solution between 5 and 7

Question

precal · Answer

Can someone remind me what the Intermediate value theorem is?

anonymous · Answer

hey,

f(x) = x(x-6)^2 -6 
we want to show
f(x) = 0 
somewhere.

since f(x) is continuous and
f(5) = -1
and 
f(7) = 1

then according to the theorem there must be some value x=a between 5 and 7 
such that f(a) = 0

anonymous · Answer

the theorem says that continuous function will get all the values between f(5) and f(7) in the interval [5,7]

precal · Answer

sorry, I was working on my review for the end of the course.

precal · Answer

ok thanks I will set it up and solve it....

precal · Answer

I just need to find the a value, correct?

precal · Answer

ok x is approximately 6.304537 got it

anonymous · Answer

no you just need to say that there is one.. not finding it

precal · Answer

ok thought I would find it