Consider the function f(x)=ln⁡(x2+3x−10) Find the domain of the function f(x) and enter your domain using paranthesis "(" , ") " or brackets "[", "]". Also, if you need the union sign U, then use the capital letter U, such as: "(1, 2) U [3, inf)" OR "(-inf, -5] U (2, inf)" The domain of ?(?)=

Q: Use adding/subtracting functions to explain why the function, w(x)=x^4 + 2x^2 - 5x  would only have…

A: Use adding/subtracting functions to explain why the function, w(x)=x4 + 2x2 - 5x would only have one…

Q: Write the length L of the rectangle as a function of y.

A: The length of the rectangle can be determined by using the fact that one end is always on y axis and…

Q: Consider the function y = (1x + 1)x. (a) Differentiate y by the product rule. (b) First, multiply…

A: (a) Differentiate y by the product rule as follows: dydx=ddxx+1x      =ddxx+1x+ddxxx+1      =1·…

Q: Given the function: f(x)=4x^2-9x, evaluate/simplify the following: f(x+h)-f(x)/h

A: Given function f(x)=4x2-9x To Evaluate f(x+h)-f(x)h

Q: Evaluate I = = / x*(x² + 4)³/ª dz

A:

Q: Evaluate the function F(x) = 4x^2-7x+7 Find f(7)

A: the solution are second step..

Q: Write f(x)=3x^3-3x in terms of y

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Q: for the function f(x)= (x+1)/(x^2+3), evaluate and simplify the following a. f(-1) b. f(2a) c.…

A: Explanation of the solution is given below..

Q: Evaluate intergral  (ax)/(x2-bx) where a and b are constants

A: The given integral is ∫axx2-bxdx.

Q: Find the inverse of the given function by completing these steps: f(x)=2x^3+4

A: Given function is f(x) =2x^3+4

Q: Rewrite each function, differentiate, and then simplify (no negative exponents!) Function Rewrite…

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Q: f(z +h)-f(z)

A:

Q: Find and simplify  f(a+h)-f(a)/h , (h does not equal 0) for the following function…

A:

Q: Evaluate the function y=-3•4^x over the domain {-2,-1,0,1,2,3}. As the values of the domain…

A: Function : It is a special type of relation form Set A to Set B (non empty sets) such that  Each…

Q: y = 2x/sqr(x^2 + 1) - find the deriviative using chain rule and explain each step clearly and show…

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.