Question

Determine whether Rolle's Theorem can be applied to the function on the given interval; if so, find the value(s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list.)

f(x) = ln(9 − sin(x)) on [0, 2π]

Answer 1

since \(\sin(0)=\sin(2\pi)=0\) you get \(f(0)=f(2\pi)=\ln(9)\) and \(\ln(9-\sin(x))\) is continuous on \([0,2\pi]\) and differentiable on the open interval so the theorem applies

Answer 2

theorem therefore says that for some number in the interval the derivative is equal to zero
take the derivative, (using the chain rule) set it equal to zero and solve

Answer 3

OH I got it thank you!

Answer 4

pi/2 and 3pi/2

Answer 5

me too

Answer 6

i mean i got that too