"If a function is continuous at some point then it must be differentiable at that point". Do you agree with this statement? Give an example with proof.

Q: Find a function in general form with a vertex at (-1, -2) and passes through (3, 6). Hint: Start…

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Q: What values of a and b make the function f continuous everywhere? x² 4 a = f(x) = and b = - " X 2…

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Q: Which statement about a function is true? (i) For each value ofx in the domain, there corresponds…

A: A function is actually a “special” kind of relationship because it follows an extra rule. Just like…

Q: Consider two functions, f and g, on the interval (-10, 10). Their graphs are depicted below:…

A: The condition of a function f(x) continuity at x=a

Q: If an odd function F has one local maximum of 5 at x=3, then what else can be said about F? Explain

A: Given that F is odd function and local maximum 5 at x=3. The aim is to state the characteristics of…

Q: Determine whether the statement " If f(x0, y0) = f(x1, y1), then x0 = x1 and y0 = y1. " ,is true or…

A: Given, the statement “if f(x0, y0) = f(x1, y1), then x0 = x1 and y0 = y1’’. We have to determine…

Q: Which of the following statements must be true for a function that is concave up everywhere?

A: Which of the  following must be there for a function than is  concave up everywhere .

Q: Explain using theorems 4, 5, 7 and/or 9 from section 2.5, why the function f(x) = sin x + Inx is…

A: Given, fx=sin x+ln x. To show that the function is continuous at every number in its domain.

Q: Over what intervals of the domain is the function positive? Negative?

A: From the given graph, it is observed that the domain of the graph is -∞,∞.

Q: A relation consists of all the points in the x-y plane that are either on the line y=1 or the line…

A: Here, the objective is to determine if equation represent a function.

Q: Give an example of a real function that is increasing on the interval (0,2), and decreasing on (2,…

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Q: Suppose that f(x) is a function with f( – 1) = – 9 and f(3) = 9. Determine which choice best…

A: given: we have a function f(x) such that f(-1)=-9 and f(3)=9. the given statement is: ''f(x)=0 for…

Q: There are 3 conditions that make a function continuous at a point.  Name the three conditions Give…

A: Definition: A function is said to be continuous at x = a provided all three of the following are…

Q: Suppose that f(E) is a continuous function with f(– 4) = – 9 and f(0) best describes the following…

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