Question

Determine if Rolle’s Theorem can be applied to f(x)=(x^2 -3x-18)/ (x-3) on the interval [-3, 6], and if it can, find all
numbers c satisfying the conclusion of that
theorem.

Answer 1

Rolles just states that if the slope of the line from a to b in the interval [a,b] is 0; then there is at least 1 place in the interval that has a tangent line that has a slope of 0

Answer 2

hmm..

Answer 3

in this case: if f(-3) = f(6); then the slope between them is 0 but, is the function continuous in the interval and does that matter?

Answer 4

yess that matters because it's part of his theorem :P

Answer 5

lol .... well, 3 goes bad in the denominator, but it maybe a hole

Answer 6

http://www.wolframalpha.com/input/?i=%28x^2+-3x-18%29%2F+%28x-3%29+

Answer 7

so is his theorem not applicable?

Answer 8

id say we have to ditch it when i see the graph. there is no way that a horizontal slope is the tangent to any part of the graph

Answer 9

hmm i see. what about xsqrt(x+18) on [-18,0]. since -18 makes the equation 0, does the theorem not work either?

Answer 10

sqrt(0) = 0

sqrt(-n) is bad

Answer 11

http://www.wolframalpha.com/input/?i=x+sqrt%28x%2B18%29

Answer 12

not bad perse as just goes unreal

Answer 13

huh?

Answer 14

-18 is not a bad x value in the equation since sqrt(0) is not undefined

Answer 15

ohhh ok

Answer 16

you will notice that f(-18) = f(0) and so has a slope of 0

Answer 17

so find the derivative of x sqrt(x+18) and equate it to 0