Let f' (x) <0 and f" (x) > 0 for all x with -o∞ < x < oo. Let (a, f(a)) and (c, f(c)) be two points on the graph of y = f(x) with a < c. What is the relationship between f(a) and f(c)? O f(a) = f(c) O f(a) < f(c) O f(a) > f(c) More information is needed.

Q: Is the function given by f(x)= X+5 continuous over the interval (-∞,0)? Why or why not? O Yes, f(x)…

A: the functionhere need to check the continuity over the given interval is contituous if

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A: It is problem of mean value theorem

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Q: Assume that for a function f(x), f'(x) « O on the interval (-0, -5) and f'(x) » O on the interval…

A: From the given definition:  f ' (x) &lt; 0 when x &lt; -5 so graph must be decreasing in this…

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Q: 4. please help!'   Calculate the domain of the function:

A: Step 1:

Q: 2) Sketch the graph of the floor function f(x) = x+31 over the interval [-4,2].

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Q: 2. Consider the function f(x) = e¯x -x5-x7 (a) Use the Intermediate Value Theorem to show that there…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.