SOLUTION: Can we apply role's theorem in the intervals [-3, 3] and [-2, 2] for the function g(x) = πx?

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Question 1184174: Can we apply role's theorem in the intervals [-3, 3] and [-2, 2] for the function g(x) = πx?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

g%28x%29+=+pi%2Ax in the intervals [-3, 3]
g%28x%29+=+pi%2Ax is continuous and differentiable on [-3, 3]
g%28-3%29+=+pi%2A%28-3%29=-3pi
g%283%29+=+pi%2A%283%29=3pi
g'%28x%29+=+pi
=> since g%28-3%29+%3C%3Eg%283%29 , role's theorem cannot be applied


g%28x%29+=+pi%2Ax
is continuous and differentiable on [-2, 2]
g%28-2%29+=+pi%2A%28-2%29=-2pi
g%282%29+=+pi%2A%282%29=2pi
g'%28x%29+=+pi
=> since g%28-2%29+%3C%3Eg%282%29+, role's theorem cannot be applied