Suppose that the functions and g are defined as follows. f(x) = -5 +3x? g (x) = 5-4x (a) Find |(-3). (b) Find all values that are NOT in the domain of If there is more than one value, separate them with commas. (a) (b) Value(s) that are NOT in the domain of :8

Q: The range of f(x)=/4-x² is [0,2] O (-00,2] [2,0) O [-2,0] [-2,2]

A: Range :- set of all output values

Q: Find f such that f ' (x) = 4x -5, f(5) = 0

A:

Q: For what value of x does the function f(x) =x³ – - 4x attain the absolute maximum in the interval…

A: Second derivative test: If the function f is twice-differentiable at a critical point x (i.e. a…

Q: Which of the functions have 5 in their domain: f(x)=x²-3x

A: Given function is f(x) = x2 - 3x

Q: Find The value of K, to Continue The function X-2 f(x)= 4-JI4+X メ+23 - %3D メ=2

A:

Q: Show that f(x)=x5-x3-1 has a zero between 1 and 2.

A:

Q: Obtain the TSE of f(x) = 2x² in powers of (x-1)

A: To Find: The Taylor Series expansion of function 2x-2 with center x=1

Q: Find the constant a such that the function is continuous on the entire real line. - [8x², a = ax -…

A:

Q: Given that f(x) = x² – 6x + 8 and = x – 2, find f(x)+ g(x) and - - express the result in standard…

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Q: The domain of f(x)=1/x is (−∞,0)∪(0,∞)(-∞,0)∪(0,∞). What is the domain of g(x)=4/x+3−7g(x)=4x+3-7?

A: Given the domain of f(x) = 1/x is (-∞ , 0) U(0 ,∞). We need to find domain of  g(x) = 4/x+3 -7 Now,…

Q: Find the domain of the function f(x) = In(4 - x2).

A:

Q: Find the domain of the function written in interval notation. f(x)= square root of x-4 divided by…

A:

Q: In the function:  f(x)= (5x)/((x^2)-25  How do you find the x-values of the inflection points?…

A: Given function is,

Q: Given that f(x)=x^2+3x-70 and g(x)=x-7, find (f-g)(x) and express the result in standard form

A:

Q: Find the domain of the function 3 - x f(x) = In x + 5 %3D

A:

Q: Find the absolute maximum and absolute minimum values of the function f(x) = -x3 + 12x + 6, over the…

A:

Q: In the function:  f(x)= (9x^2)/ ((x^2)-49) Indicate the domain and range in interval notation.  What…

A: Denominator of the function can not be equal to 0.

Q: The graph of f (x)3-x²-5x+6 has the point (2, -6) on it. O True O False

A: Given statement  The graph of f(x)=-x^2-5x+6 has the point (2,-6) on it

Q: Use the intermediate value theorem to show that the function f(x) = x³ – 3x + 1 has an x-intercept

A: Intermediate value theorem

Q: 7. Find the domain of f(x) = V² + 2x – 3 and write it in interval notation.

A: The solution is given below.

Q: Find f(x) =2x2+3x-5, then prove that f'(0) +3f'(-1)=0

A: Givenfx=2x2+3x−5To provef'0 +3f'−1=0

Q: Determine the number of possible positive and negative zeros for the given function in accordance…

A: To determine the number of possible positive and negative zeros of the function.

Q: For the function f(x)= x3 + ax2 + 2a2x + a, there exists a point of inflection at x = 2. Determine…

A:

Q: • The domain of f (x) 3-х is 1+x2 1. R 2. R/{1,-1} 3. R/{3} 4. (0, 00)

A:

Q: f(x) = x3 -3x2 - 3x +1 x=-1 is a root of the function how would you show that?

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Q: 1. Let f (x) = 2x² – x – 1 and let g(x) = x – 1 Which statement is true?

A: Given, f(x)=2x2-x-1 and g(x)=x-1

Q: For the f(x)=−x3+3x+6f(x)=−x3+3x+6 determine the coordinates of the turning point(s) and any…

A: See the attachment

Q: Let f(x)=x−3x−−√3f(x)=x−3x3 Can you please show me how to find the inflection points and the local…

A: Given that : f(x) = x - x3

Q: Find (f-g)(x) if f(x)=sqrt16x4 and g(x)=3x3-3x-5. Choose from the answers below.…

A:

Q: The function f is defined by f:x --> 10-(x-3)² for 2

A: To find: The value of function at . Calculation: Substitute in function.

Q: What happens to function f(x) ( 1+x2) 1/x2 as x approches to zero

A: The restrict of a feature is a essential belief in calculus and evaluation that describes how the…

Q: inflection point if any of the function  g(x)=9x^3 - 4x

A: Inflection point of given function is (0, 0)

Q: Find the all extreme points of f(x) = x³ – 6x2 + 9x – 3 is or [-2, 2] ? |

A:

Q: Explain why the function has at least one zero in the given interval.

A: To explain why the given function has at least one zero in the given interval.

Q: Suppose that f'(x) = g'(x) for all real numbers. Explain why there is a constant c so that f(x) –…

A: We need to show that why there is a constant c so that f(x)-g(x)=c for all real numbers.

Q: The domain and the rang of the - * function In (x - 2) are

A: the log function is not defined for zero and negative numbers so the value of x-1 should be greater…

Q: The domain of f(x)=1xf(x)=1x is (−∞,0)∪(0,∞)(-∞,0)∪(0,∞). What is the domain of…

A:

Q: Suppose k>0. What is the domain of F(x) =/k² – x² ?

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Q: 1. When the function f(x) is divided by x + 2, the quotient is x2 -x -8 and the remainder is -3.…

A:

Q: Find and classify the extreme values of f(x) = 6x4 – 4x over the interval [-2, 2].

A:

Q: Find the domain and range of the function: 1 1- V5 - x

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Q: 7. Find and simplify the difference quotient f(x+h)-f(x) for the function f(x) = x² -

A: I am answering first question

Q: Find f such that f'(x) = 8x + 3x - 3 and f(0) = 4. %3D

A:

Q: Let f(x) = x + 10 and g(x) = x² – 9. Find the domain of (-) (x)

A: Solution of the problem as follows

Q: Find f (x) for the function f(x) = х-2 ·In x+5

A: This question can be solved using the concept of inverse of function.

Q: absolute extremum of the function on the given interval.

A: Absolute Extremum:- Suppose f is function on interval a,b then,i the y-value fc is an absolute…

Q: Find the extreme values of the function f(x) = (x² + 2x)³ on the interval [-2, 1].

A:

Q: Determine all the points of inflections of the function f (x) ex²-2x²-5x + 8

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Q: 3 Let f(x) = 4.x² 5 and g(x)= 3.x + 7, find. -

A:

Q: Explain why the function has at least one zero in the given interval.          Function f(x) = x3 +…

A: Given: fx=x3+5x-3

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.