Consider a convex function f : R → R. Recall that f is convex if f(tx + (1– t)y) 0. • Prove that for any n f (a1x1+ a2x2 + +an&n} < aif(¤1}+ a2f(x2) + … + anf(xn} where a1 + a2 + · · ·+ an = 1, where a; > 0.

Q: Are the following functions quasi-concave? Assume x ≥ 0 a) f(x) = a b) f(x) = a + cx², c < 0

A: Both questions are different so I soved 1st queation if you want 2nd one then repost it again.

Q: Let f(x) f-¹(x) = 1 x + 11

A: we need to find the inverse of the function.

Q: If f(x) =-3x, Show that f (x) satisfies the hypothesis of the Roll's Theorem on the interval [-3, 3]

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Q: 3. Find the largest domain (in R2) for the function In(3 + y) 1- x + y f (x, y) :

A: Let's find.

Q: Draw the graph of the function f :R → R defined by f (x) = x3, x∈R.

A: We will make a table for f(x)=x3 x -1 0 1 y -1 0 1

Q: Q2.) Determine if f(x) is convex, concave, or none of these also state if it attains a max. or a…

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Q: Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)²,…

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Q: Sketch the graph of f

A: Given: f(x)=lnx

Q: Show that the real-valued function f: R → R defined by f(x) = x° x E R. 3x2 + 3x + 1 increases for…

A: Answer

Q: 3. Let f : R→R be a function defined by f(r) = 2x + 1. Is this function (only) injective, (only)…

A: Let us consider the function f: A→B then the function is said to be  Injective or one-one :That is…

Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

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Q: Prove that the linear function f(x) = ax+b is continuous.

A: To prove that the given linear function is continuous.

Q: e) If a convex function f: R→ R satisfies f(10) value for f(7)? = -4 and f(20) = 30, what's the…

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Q: z) = (x2 + then (a + E

A:

Q: f(2) = 4 and f(3) = 3. With this information, can you determine whether there exists a real number c…

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Q: Find the x that maximizes the function f defined as f(x) = x¹/2 - 2x 1/3 1/4 O 1/8 1/16

A: The derivative will be zero at the minimum and maximum points because the line turns to be parallel…

Q: Fxy(x, y) is a monotonic and non-decreasing function of both x and y.

A:

Q: Find all global minimum points of ƒ in R³, if ƒ (x1, x2, x3) = ex² + x½ + 2x²x3 + x² − 8x2 - 8x3

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Q: Suppose that F(x) is a function such that F"(x) = f(x). Which of the following statements is true? […

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Q: Given the function f(x) = x - 4x + 5x, then the interval(s) where f (x) 1s concave down: A. (-0). B.…

A: As in concave down the second derivative of the function is negative

Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

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Q: Given the second order differential equation that models the motion of a harmonic answer the…

A: Given : A second-order differential equation x''+6x'+9x=0 that models the motion of a harmonic…

Q: . Let ƒ(x) = (x² - 4)³. Do the following. (a) Find the maximum value and the minimum value of f on…

A: We have to solve given Questions.

Q: 2. Let us define a. Verify that f(x, y) = c. Now consider the function git Similarly, consider the…

A: Given Data: Let us consider the given function is fx,y=xyx2-y2x2+y2

Q: Use the nodes ro = a - ya and r1 = a + ya to linearly interpolate a function f(r) on the interval [a…

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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.