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9 Nov 2019
Your help with this is greatly appreciated!!!!!
f(x) is a function that is continuous on [0,1] and differentiable on (0,1) with f(0) = f(l) = 0 .Treat each numbered problem as a "new" f(x) so the numbered properties listed are NOT cumulative and are NOT intended to all describe the same function. Importantly, f(x) could be, but does NOT have to be, a polynomial. BONUS: A set of reasonable responses earns an extra attempt at an exam of your choice this semester. What does Rolle's Theorem tell you about f (x) in the interval (0,1)? Suppose you are told that |f (x) | 1 for all x in the interval (0,l) . What can be concluded about the values of the first derivative f(x) in the interval (0,1) ? Note: part a is needed to draw a conclusion. Suppose you are told that |f (x) | 1 for all x in the interval (0,1). You drew conclusions about f(x) in part b. What can be concluded about the values of f(x) on the interval (0,1)?
Your help with this is greatly appreciated!!!!!
f(x) is a function that is continuous on [0,1] and differentiable on (0,1) with f(0) = f(l) = 0 .Treat each numbered problem as a "new" f(x) so the numbered properties listed are NOT cumulative and are NOT intended to all describe the same function. Importantly, f(x) could be, but does NOT have to be, a polynomial. BONUS: A set of reasonable responses earns an extra attempt at an exam of your choice this semester. What does Rolle's Theorem tell you about f (x) in the interval (0,1)? Suppose you are told that |f (x) | 1 for all x in the interval (0,l) . What can be concluded about the values of the first derivative f(x) in the interval (0,1) ? Note: part a is needed to draw a conclusion. Suppose you are told that |f (x) | 1 for all x in the interval (0,1). You drew conclusions about f(x) in part b. What can be concluded about the values of f(x) on the interval (0,1)?