2.Produce graphs of f that reveal all the important aspects of the curve. Then use calculus to find the intervals of increase and decrease and the intervals of concavity. (Enter your answers in interval notation. Do not round your answers.) f(x) = (1/x^12)-(2x10^6/x^6) 2a)find the interval of increase and decrease 2b)find the interval where the function is concave up and concave down

Q: A function y with the property that y = -y" is

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Q: a) y = -3f(x) Domain: Submit Answer Incorrect. Tries 1/99 Previous Tries Range: Submit Answer Tries…

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Q: given the function: y = x^3 + 2x^2 + x + 1 a. Find intervals where the function is increasing and…

A: In the question it is asked to conclude some points for the function given.

Q: Sketch the curve of the function f(x) = (x² – 4x – 5)/(x² + x) %3D - SHOW ALL WORK FOR THE FOLLOWING…

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Q: 1) Let f(x) be a function with Domain [-6,-2] and  Range [-10,-4]. Find the domain and range of the…

A: Given that for f(x) Domain [-6,-2] and  Range [-10,-4]

Q: Determine whether the function has a concave up and/or concave down. f(x)=x/5+x^2

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Q: 7. Give two reasons why a function might not be differentiable at a particular value of x.

A: topic -derivative

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.