Let f(x) = x^2/√x−10 + 1/2x−30. Find the domain of f

Q: Find f(-2) for f(x)=3x2^x

A: f(x) = 3x2^x we can also write this as f(x)=3x(2x)

Q: Let f(x) = 5x^3 + x + 1. If f(2) = 43, then (x − 2) is a factor of f(x).

A: f(x) =5x3+x+1

Q: Given the function f(x)

A: Given,          f(x)=3x2-5x+3

Q: find the interval where the function is increasing or decreasing  f(x) = 6/x-4

A: Function is not defined at x=4  there are two intervals where the function is defined   ( -∞,4 ) and…

Q: Find f^-1(x) for f(x)=13+14x

A: Explanation of the answer is as follows

Q: Differentiate the function y=1lnx.

A: Given function is y=1·lnx We know that any number multiply with 1 gives same number. So, function is…

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

A:

Q: Find the value of g(x)=√x^2 - 2 if g(x)= -3.

A: find       g(x)= -3.

Q: Given f(x)=3x^2 + 4x + 5, determine the roots of the function. Verify them with a graph.

A: An algebraic expression is obtained by combining numbers and variables together with arithmetic…

Q: Consider the function f(x)=5√x+9x^3+6x f′(x)=

A:

Q: List the zero's of f(x) = x³ + 3x² - 4x. X =

A:

Q: find x: sec² 2x = 4

A:

Q: Find the first and second differences of equation f(x) = 10 – (4 – x)^2. Is it a quadratic function?

A:

Q: downward and 2 units to the left f(x)=-2(x+1)^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.