Suppose that the functions s and t are defined for all real numbers x as follows. s(x) =x-1 t(x)= 4x+4 Write the expressions for (s-t) (x) and (s+t)(x) and evaluate (s-t)(-2). (s - 1)(x) = 0 (s+ )(x) = D (s-)(-2) = 0 %3D %3D %3D

Q: Find a formula for the exponentail function passing through the points (-2,40) and (1,5)

A: The general equation for an exponential equation is  y = a(b)x

Q: Find n(B) if B = {x : x is a letter in the word “bookkeeper”}.

A: Find n(B) if B = {x : x is a letter in the word “bookkeeper”}.

Q: Differentiate. f(x) = (x 2 - 2x + 4)ex O ex(x² + 2) O ex(x² + 4x + 2) 3 +x+4 O ex(2x - 2)

A: Given the function fx=x2-2x+4ex

Q: Give the domain for t(x)= x+1/x2-3x-18

A: Given function is,

Q: Choose all functions that are members of the same family. Oy=-x(x − 3)(x + 5) Oy=x³ + 2x² - 15x…

A: By simplifying each function, we can identify the members of same family.

Q: Let f(x)=x +3 and g(x)=-2x+6. Find each of the following. (a) (f+g)(2) (b) (S - 8)X2) (c) (fg)(2)…

A: we have to find the following

Q: Evaluate ((x-2)/x dx : 4 O 6 .6 テメ 11 3 11 * + C 11 6 4 + C 11 * テ x² +C /6

A:

Q: Let f(x) =-3x+4 and g(x) =-x² +4x+1. Find and simplify each of the following. (5) f(-x) (6) gt-)

A: In function  f(x) ,X replace by -x and function g(x),x replace by -1/4.

Q: f(x)={x2-9/x-3 if x is not 3.  7 if x=3

A:

Q: Let /(x) = 7 - 9x - 20. Find f(-3)

A:

Q: of the 7x - 9x-2

A: We have to choose the correct answer from the given options

Q: Calculate the value of n if f(x) = (8 - x)*/3 and 16" = f(16).

A:

Q: Differentiate. f(x) = In (4x + 1)(x+7)³ (1 - 6x)5

A: The solution is given below:

Q: Find f1(-2) whenever f(x)= x2+2x-1/ex

A: We are given f(x)= x2+2x-1/ex. Here, we need to find f1(-2) that is nothing but finding f(-2).

Q: Draw y² = f(x) 1+ (1,-1) 2 (2.5,1)

A: We have draw the graph of y2=f(x)The procedure is given below

Q: [f^(x) = 1/² + If and f-¹ (5) = 6, find k.

A:

Q: If ƒ (x) = (2x+1) ³ (x-3) 4 4 then f(0) =

A: Given:    f(x) = 2x+13x-34

Q: Find p(- 2) and p(3) for function p(x) = x ^ 3 - x ^ 5

A: We have given function as  p(x)=x3-x5   We have to find p(-2) And p(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.