Let f(x) be a differentiable function and g(x)=(ƒ(x))³ – 3(f(x))² + 4f(x) + 5x + 3sin x + 4cos x V x € R, then prove that g is increasing whenever fis increasing.

Q: (3-х, х <2 +1, x 2 2 B. Is the function h(x) continuous at x-2?

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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: Exercise 1. Let f(x) be the function 2х — 1 if x 2. - (a) Find the value of c that makes f(x)…

A: Given f(x)=2x-1if x&lt;-1cxif -1≤x≤2x-2if x&gt;2

Q: determine the continuity of the function at a.

A: The objective of this question is to determine whether the function f(x) = 1/(x + 2) is continuous…

Q: 02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated…

A: Answer

Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

A: Let z = x+iy then Re(z) = x and |z| = √(x^2 + y^2) If z = 0 =&gt; x = 0 and y = 0

Q: Determine and graph the domain set of the function f(x, y) = ln(x²+9y2-81) ==

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Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: The function f(x) = 6e-2x is concave upward over the interval: a b C Od (1, +∞0) (-∞, +∞0) (-∞0, 0)…

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Q: Explain why there does not exist differentiable functions f and g for which f(0) = g(0) = 0 and =…

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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: In(2 - a) x² + y² – 16' Determine the domain of the function f(x, y)

A: The domain of a function is the values of the variables of the function that result in a defined…

Q: Given the function h(x) = x² + 6x + 5, determine the average rate of change of the function over the…

A: The average rate of change of the function f(x) is given by the formula f(b)-f(a)b-a. Here, the…

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: Show that f(x) = e describes a bijective function from R to (0,+x). (a) Show that f is a function.…

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Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: u+iv is analytic function, under what condition (if any) v+iu

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Q: Show that the function f(x)=x|x| is continuous and differentiable at x = 0

A: To show that f(x)=xx is continuous at x=0 To show that limx→0xx=00=0 use piecewise definition for…

Q: 3. (a) Prove that the function f : R → R, ƒ(x) = 4x² −14x¹+30x-17, is injective. (b) Find the…

A: The answer to this question is given below.Explanation:

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

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Q: Find the explicit general solution to the following differential equation. A prime denotes a…

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Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2