True or False?

IF f is continuous on [2,4], f' exists on (2,4) and f'(c)=(f(4)-f(2))/2, then cE(2,4)

i think E means "belongs to"

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

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