(5) Let f: RR be twice-differentiable f(x) ≤0 and Prove that f is constant on R. on R. Suppose that f"(x) ≥0 for all x = R

Q: If f"(x)>0 on an interval I then...

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Q: If f is even, then f' is even.

A: The question is taken from the function in which we have to do that f is even then its derivative is…

Q: Assume that is differentiable on a ≤ x ≤ b and that f (b) < f (a). Show that f' is negative at some…

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Q: Determine if = f(x)=Vxis uniformly continous on the interval I [0, +)

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Q: 1. Let h : R → R be some twice-differentiable function. Define f(x,y) =h() for all x ≠ 0. Show that…

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Q: 10. Let F(x, y) = 1 + v4 – y². (a) Evaluate F(3, 1). (b) Find and sketch the domain of F. (c) Find…

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Q: Determine L[f]if 0, f(1) = {1- 1, 0 2. 1,

A: Given that, A function f(t), t ≥ 0, its Laplace transform F(s) = L{f(t)} is defined as

Q: Define f: R-&gt;R as follows: f(x)=x-[x] if [x] is even. f(x)=x-[x+1] if [x] is odd. Determine those…

A: To find the points where the given function is continuous.Take two cases:Case 1: Let x = a is an…

Q: (-) = { 2*. x 2 Find the values of a and b so that f will be differentiable at x = 2.

A: Given function is fx=7x2        ,x≤2ax+b    ,x&gt;2. By continuity, 722=a2+b74=2a+b2a+b=28     ...1…

Q: Let f(x) = x° – 2, -1< x < 3 The domain ofƒ¯is the interval [A, B]| where A = and B =

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Q: 6. Prove that f(x)=√x is continuous for all x ≥ 0.

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Q: Let f: X --> Y be a function, and let U be a subset of X.  (1) Prove or disprove that f maps X \ U…

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Q: If f is continuous on the interval [5, 12] and f(5) = 7 and f(12) = -2, then f must have at least…

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Q: Let the region R be the area enclosed by the function f (x) = ln (x) and g(x) = x – 2. If the region…

A: To find the length of the side of a square, compute the vertical distance between two curves fx=lnx…

Q: Draw the level curves for the function f(x,y) = x2-y. Show five level curves within the limits…

A: We shall use MATLAB to solve the above problem.We are using computer code so that it will be very…

Q: Let f(x) = x5 + 5x4 + 6x + 3.   a. Conduct a sign analysis of f''. That is, determine the sign of…

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Q: Show that if f"(x) < 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] < favg < f[(a+b)/2]

A: Consider the given information. f"(x) &lt; 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] &lt; favg &lt;…