The key statement is essentially "if the slope of f at point c is equal to the slope between points f(2) and f(4), then c is between 2 and 4". This disproved with a simple linear function f(x) = x. if f'(c) = (f(4) - f(2)) / 2 = 1, then c is any real number, not just limited to (2,4).
Note that there must be at least one solution c that lies in the range (2,4), however the claim is that -all- solutions c lie within (2,4), which is incorrect.
Comments
False.
The key statement is essentially "if the slope of f at point c is equal to the slope between points f(2) and f(4), then c is between 2 and 4". This disproved with a simple linear function f(x) = x. if f'(c) = (f(4) - f(2)) / 2 = 1, then c is any real number, not just limited to (2,4).
Note that there must be at least one solution c that lies in the range (2,4), however the claim is that -all- solutions c lie within (2,4), which is incorrect.
uh......false?sorry I really don't know I just wanna answer some questions!
true