Assume the functions below are continuous with domain all real numbers. (a) If f'(a) = 0, then x = a must be a local minimum or local maximum of f. O True O False (b) If g'(a) is undefined, then x = a could be a local maximum or local minimum of g. O True O False

Q: Which of the following is the absolute minimum value of the fuk took f(x)=(x-3)^3 on interval [1,4]

A: The graph is shown below:

Q: Verify that the three conditions of the hypothesis of Rolle's Theorem hold for the function f (x) =…

A: 1. f(x) is continuous on the closed interval [a,b] 2. f(x) is differentiable on the open interval…

Q: 75. Show that if a function f is defined on an interval symmetric about the origin (so that f is…

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Q: Determine if the following relations describe a function. Justify your answer. a) R1 = {(1,8), (2,…

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Q: ,for x 1 Discuss the contuniuty of f andf'.

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Q: 5. Ôx (@) = ¢x (- w), if X is symmetric function.

A:

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: Which of the following are generally NOT true, for any given function f:X-->Y and subsets A and B of…

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Q: PROVE THAT Q(-∞) =1 usign Q – Function

A: Given that Q-∞=1

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…