If f(x)= 2x2 + 3x +1 and g(x)= 2x+1 (f - 8)(-2) (f xg)(-2) (x)

Q: AY (x) 10-8 6 -4 2 2- g(x) 4.

A:

Q: What is g'(x) when g(x) = 1 3z²+6z+7 2z²+2x³

A:

Q: (a): Find the critical points of the function f(x) = 8x² – 16x.

A:

Q: x² - x - 12 f (x) = x2 - 2x- 8

A: In the question function given is-        f(x)=x2-x-12x2-2x-8 Simplifying the given function we get-…

Q: 2x - 3x + 13x+a if x#2 f(x) = . X-2 b if x = 2

A: Solution:- It is give that f(x) is continuous at x=2  and the given function is  f(x)=…

Q: f(x) = x3 + x2 - 6x y 30- g(x) = 6x 20+ (3, 18) 10+ -10+ -20- (-4, -24) -30- 2.

A:

Q: V7x+2-V6x+4 = )f(x مستمرة عند 2 = ۲ if x 2 and x # 2 1- قيمة الثابت الذي يجعل الداله (x-2) if x = 2

A: Continuous at x=2,  using rationalization

Q: f(x)= 2x+5 3x-2 -19 (3x-2) f(x)=-

A: SOLUTION-

Q: X-3 1-7X ガ ニ ー4x2 f-14X4|l 5-X if x>l

A:

Q: Find the domain of f(x)=ln(4x-20)+ln(x 2+9x+18)

A:

Q: 2 f(x) = √2x + x².

A:

Q: x2 - 6x - 7 4x2 + x - 3 f(x)

A: Remark: Vertical Asymptotes The line x= L is a vertical asymptote of yhe the function y=f(x), if the…

Q: 2) Find f'(x) if f(x) = 6x¬2 + 8x3 + 11x.

A: We have to find f'(x) where f(x)=6x-2+8x3+11x.

Q: [3] If f(2x+3)=4x²-2x+3, find f(x)

A: Firstly put t=2x +3 and find f(t) ,After that replace 't' as 'x'.

Q: A firm can produce only 3200 units per month. The monthly total cost is given by C(x) = 400 + 200x…

A:

Q: The maximum number of turning points possible for f(x) = 3x" – 6z² + 5x – 31, is

A:

Q: If f(x) = 5x6 - 2x² then [f(x)dx=

A: The given function is: f(x)=5x6-2x4

Q: 2- 1y = f(x)} -4 -2 2 -2-

A:

Q: 1. f(x) = - 6x² + 11x - 3.2

A:

Q: If f(x) = 5x' +x²+ 4, then f(-2)- --

A: Given : fx = 5x3+x2+4

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: Find f’(-2) if f(x) =4x^2(8x-3)^4

A: Given that, Find f’(-2) if f(x) =4x^2(8x-3)^4 To find the derivative of f(x)

Q: If f(x) = 2x3 + Ax2 + 4x - 5 and f(2) = 5, what is thevalue of A ?

A:

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

A:

Q: Differentiate f(x)=(3x^(8)-x^(-2/3))(6x^(1/3)-e^(3x))

A:

Q: Sketch the graph of:

A:

Q: 1. Use synthetic substitution to find f (-2) if ƒ (x) = 2x* – 5x³ – x + 13.

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Determine the critical points of f(x) = 8x3+81x2−42x−8.

A:

Q: Find sum of two polynomial f(x) = x^3-7x+6 and g(x) = 5x^3-8x+1

A:

Q: Analyze the critical points of f (x) = x5 − 5x4.

A: To analyze the critical points of f (x) = x5 − 5x4.

Q: f(x) = ×2 + 2x - 2 then f(-2) =

A: Given query is to find the value of the function at indicated point.

Q: 2. How many, and what type, of solutions exist for the function f(x) = x - 3x- 27x + 19x² +114x-72?

A: Given: f(x)=x5-3x4-27x3+19x2+114x-72

Q: (x3-2x)²(1-2x)ž f(x) (3x-4)*

A:

Q: F(x) = 3x2 +4x -5 G(x) = 2x2-8 H(x) = -4x2 +5x-2       F(2) - H(-3)

A: Substitute the value of x for each function and find F(2) - H(-3). As F(x) is given, put x= 2 to…

Q: f(x) =-2x - 4 if xs2 |4x -9 if x> 2 3.

A:

Q: (-1, xS-4 2) f(x) = {2x + 2,-4 0 -8 64-2

A: We have to find the graph of the given function

Q: Find critical point of f(x)= 24x^2/3-8x

A: Find derivative of given function.

Q: Differentiate f(x) = x² – 3x by first principles“

A: Given f(x)=x2-3x

Q: 1. If f(x) = 5x4 - 6x² + 4x2 find f'(x) and f'(2).

A:

Q: 2. f(x) = 3x - 1; g(x) = 4 – 2x

A:

Q: x)=x^4-2x^2-24

A:

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

A:

Q: -9x(x-2) 8. g(x)=(x²-3x² +1)* 8'(x) =. (2-3x²+1) 2x+1 (3x-1) 9. f(x)=2 _ 6(x² +10x+1) (x+5)* f'(x)…

A:

Q: Find f(-3) whenf (x) = 2x2 +2

A: Solution of the problem as follows

Q: Find f'''(-3) f(x)=4x^5-3x^4+5x^2-15

A:

Q: If f'(x)=2x5-8x3+10cosx then state a possibility for the equation of f(x).

A:

Q: F(x) = 2x^3 -11x^2 -7x+6 and X=-1 is a solution,

A: Put value in function if get 0 then this the solution

Q: 2. Find f'(x) if f(x) = (x³)(8x² – 4) -

A: Given,

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.