f(x) = , f (x) = , "(x) = 2-0) X-2 %3D 4-X 2(x-6) f" (x) %3D x3 x4

Q: f(x) = 3x + 4; g(x) = f(-x) %3D %3D

A:

Q: G-Xモ-(X))

A: f(x)=2x-5   Replace x = x-5   f(x-5) = 2(x-5)-5 f(x-5) = 2x-10-5 f(x-5) = 2x-15

Q: x+8 f(x) = 6x-8, g(x)= %3D

A:

Q: A- TI x + 2 x² – 3x – 10 51. f(x) x + 2| 53. f(x) : x + 2 х, 55. f(x) : x, xs 1 [x², x > 1 %3D x +…

A:

Q: 9. h(x) = (x2-4) (x2-1) 10. g(x) = %3D -5x-23x3-25x2-x+ 6

A: Given: The given curve is hx=x6-8x5+24x4-32x3+16x2. To find: The main aim is to sketch the graph of…

Q: 7. f(x) = x³ + 7x + 1

A: To find the end behavior of f(x)=x8+7x+1.   End behavior definition: The end behavior of a function…

Q: -343x x = -2 g(x) = { (x – 1)(x+ 2) x = -1 | a3 – 22 +1 , x + -2, –1 g(1) =

A:

Q: . f(x) = 5x + 2; g(x): -2) - f(x) =x - 7; g(x) = 2x + 14

A:

Q: 5. f (x) = -x² (3x + 7)(x – 2)(x + 1) %3D

A: We have given f(x) = -x2(3x+7)(x-2)(x+1)  We have to find  1) roots of this function 2) end…

Q: f(x) = 3x + 5 g(x) = 4x² – 2 %3D h(x) = x² – 3x + 1 Find f(x) - g(x) – h(x). O - 5x + 6x + 6 O -5x +…

A:

Q: f(x) = 4√√x + 2x¹/2 - 8x-7/8 +x². f(x) +2 1 x3 = ²325/2 - 2x³/2+1/32²³- x³ - 2x² + x −1. 9

A:

Q: The population of a city is expected to be P(x) = x(x2 + 16)-1/2 million people after x years. Find…

A:

Q: 3 + 2x g(x) %3D 5 - 8x

A:

Q: x5-3x-2-7x c) iii) f"(x) for f(x) = %3D

A:

Q: f(x)= 2x^2 -5x+4 f(x+3)=

A: Substitute x+3 in place of x in the given equation. f(x+3)=2(x+3)2-5(x+3)+4

Q: Integration of (x+4)/(6x – 7 – x²)

A:

Q: the integration of : f(x) = - 2x+4/(x^2+1)(x^2-4).

A:

Q: x -> 0

A:

Q: x2 -16 f(x) = continous at x = 4. %3D x2 -3x-4

A: f(x) = x2-16x2-3x-4 continous at x=4 This can be solved using factorization of quadratic equation

Q: 26) g(x) = x² – 5x; g(x) = 104. Find x. %3D -

A:

Q: f(x)= x^2-4x g(x)= x^2+3x+8

A:

Q: f(x) = x^2 - 12x + 35 g(x)= x -5 (f+g)(-4) = (f-g) (-5) =

A:

Q: F(x)=e^2x (3x^2-x)

A: see 2nd step

Q: f(x) =x² - &r+4 g (x) = 4x – 3 h(x) =x+2 1) (+g)(x)= |2) - h)(x) = 3) (hg)(x) =…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: -f(x) = x2 +3x-40

A:

Q: f(x) = 4x + 1 g(x) = 3x - 5

A:

Q: 1. f(x) = x², g(x) = 6-x 2. f(x) = x+ + 2x², 3. f(x) = 3+√√2x_g(x)=x-1 g(x) = 6x²

A: Since you have posted multiple subparts question in this question so i have solved the first three…

Q: f(x)=x2-2x+4     g(x)=x2+2x-4 (f o g)(4)

A:

Q: Sketch the graph of f.

A: Given,           fx=x3-2x2-4x+8x-2

Q: X-2 9) f(x) = %3D x2 - x - 30

A:

Q: 4. f(x) = x² + 4x 5 %3D -

A: As per our guidelines we are supposed to answer only first three parts.kindly repost others part as…

Q: 8) f(x) = 2x + 5; g(x) = 3x - 1 Find bo

A: Givenf(x)=2x+5g(x)=3x-1

Q: f'(x) = -2xe f"(x) = (4x² – 2)e- f(4) (x) = 4e* f(3) (x) = -4xe-" (2x² – 3) (3 –12x² + 4x*)

A:

Q: x-2, xS-2 3) f(x) = %3D (-x-3, x>-2

A:

Q: f (x) = 3x + 5 f(g(x)) g(x) = x – 7 3x - 2 3x - 26 3x - 16 4x - 2

A:

Q: f(x)= -4x g(x)=3x-2 h(x)=x^2-6x. solve: f(x)+g(x)

A: To find the f(x)+g(x)

Q: max F(x1 ,x2) = x,x3 subject to 6xỉ + 3x = 72

A: Let the given function be  F(x1,x2)=x1x22    ….(1) and  G(x1,x2)=6x12+3x22-72=0    …(2) From…

Q: 4. f(x) 5. f(x) = 8 - 25x 3x²+5x-20 [-3, 3] (-2, 2)

A: To find the extrema of the following functions :-

Q: f(x)=4x-3, g(x)=x+4, (f+g)(x)=

A:

Q: x2 + x - 7 f(x) = %3D x² - 7 f'(x) = %3D

A: We have f(x)=x2+x-7x2-7 By quotient rule, we get

Q: (fog)(x). f(x)=x2+4 and g(x)=x2-7

A: Given data:   The first function is f(x)=x2+4. The second function is g(x)=x2-7.   The expression…

Q: F(x)=1/3x^3-1/2x^2-12x+4 Domain [-4,5] F’(x)=x^2-x-12

A: To find the correct option

Q: 2 f(x) = x² - 9 %3D (- 4,f(– 4)) = (0,f(0)) = (4,f(4)) =

A: Given that  f(x) = 2/(x2 - 9)  We need to find the following points. Now, f(-4) = 2/((-4)2 - 9)…

Q: 3. f(x)=5x-3 g(x)=(x-1)2 %3D

A: Here, the given functions are: f(x)=5x-3, g(x)=(x-1)2 To find g(f(3)).

Q: Зx2 - %3D 5x + 2 H(x) х2 - 1

A: we have been given the function H(x) H(x)=3x2-5x+2x2-1we have to find the value H(3)=limx→3H(x)  and…

Q: 6. f(x) = x² – 4x, g(x) = 2-3E %3D a) (f - g)(-5)

A: Given: f(x)=x2−4xg(x)=2−3x

Q: 1. Find fog. f (x) = -4x + 6 A) (fog)(x) =-5x B) (fog)(x) =-4x² + 30x – 36 C) (fog)(x) =-4x + 30 g…

A: f(x)=-4x+6g(x)=x-6

Q: 3. f(x) = x³- 2x + 3x-3 4. f(x) = 8x +

A:

Q: :h(x) = f(g(x)) %3D 1) h(x) = x2-5 2) h(x) : +3 x2-7 3) h(x) = (x2 + 5x – 1)700

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: 5. f(x) = x²(3x + 2)³; f'(-2)

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.