If f(x) = 3x4 + 4x³ – 12x² + 12, then f(x) is (1) increasing in (-∞, - 2) and in (0, 1) (2) increasing in (-2, 0) and in (1, 0) (3) decreasing in (-2, 0) and in (0, 1) (4) decreasing in (-∞, -2) and in (1, ∞)

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A:

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A: fx=ex+3x+ln4

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A: The given function is  f(x) = 12x3

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A:

Q: (15) If X-exp(1), then (a) 2X-exp(2) (c) 2x~exp (¹) O a O b O C Od (b) 2X-X² (2) (d) 2X-G(2,1) is

A: Given that X~exp(1) then  We have to find 2X follows which distribution:

Q: e*+1 Differentiate the function f(x)= In -3x +1 -3e A) 4e** +1 +1 3e B) e +1 +1 3e C) 3x 1. D) E) +1

A: Topic: differentiation

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A: Given query is to find the derivative of the expression.

Q: 2. If f(x) = ((-4,4) (-3,0)(-2,8)(-1,-2)(0,-4) (1,5)) and g(x) = {(-3,0)(-1,6) (1,-4)(3,-2)),…

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A: Given a graph for various values of x and y. We need to find: As x→4, k(x)→ As x→−10, k(x)→

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A: We have to find functional value.

Q: C Chain Rule 7) f (x )> (2x +5)

A: To determine the derivative using chain rule.

Q: If f(x) = x(e*+=') , then f'(x) = %3D %3D (A) (e² + æ³) æ(e*+z*-1) (B) (e" + 5æª) In(x) æ(e*+a*) (C)…

A: We have to find derivative of f(x).

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Q: Suppose P(z) is a polynomial satisfying • P(5) = - 5 P'(5) P"(5) = - 156 Р(3) (5) 3D — 414 305

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A:

Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

A: See the attachment

Q: Differentiate y = In(x³ + e*) .2 3x+eX А. x3+e-X 3x2-ex В. x3 +e-X 3x2-e-x C. x3-e-X 3x2-e-x D.…

A:

Q: 4. y = (4t2 - t)(t³ – 8t² + 12) 5. h(z) = (1+ 2z + 3z?)(5z + 8z² – z³) %3D - %3D

A: To differentiate the following functions.4 y=4t2-tt3-8t2+125 hz=1+2z+3z25z+8z2-z3

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A:

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Q: EXAMPLE 3 If f(2) = 5, (4) = 6, and f(7) = -9, find f -'(6), f ·'(5), and f '(-9). SOLUTION -1 From…

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Q: 6. Show that when 0 < |-1|< 2, (z-1)(z-3) Complex Analysis (z-1)" 2+2 =-36 z−3) ² A=0 2(z-1)

A: We use substitution and Laurent series expansion.

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Q: If 6x³ +x* –y³ 2x² +y² f(x, y)= if (x, y) (0, 0) if (x, y)= (0, 0) then f,(0, 0)= O does not exist

A: Thanks for the question :)And your upvote will be really appreciable ;) Correct option (A) does not…

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A:

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Q: 2.) f(x) = 2x + 4x + 2x + 1 %3D 31 2 g(x) = x - x + 7x +9 Find (f + g)(1)

A: Topic - functions