Find the local maximum and minimum values of f using both the First and Second Derivative Tests. f(x) : = 9 + 3x2 – 2x3 local maximum value local minimum value

Q: Find the points of inflection of the function f(x)=esinx.

A: Inflection point is the point where concavity of graph of function changes. At this point double…

Q: Find f(x).

A: Given,

Q: The function f is given by f (x) = (1+x)=. How do the values of f behave for small positive and…

A: Here we define  f  for small or large positive value of x.

Q: You know f:J→J and g: J→J Select the choice with algebraic expression for f and g such that f(g(x))…

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Q: What type of discontinuity does the function f(x)=xsecx have?

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Q: Let f be a function. Explain, using any method , as to why f(x) and f(x) + 2 have the same…

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Q: Is the function g(x) = x2 one-to-one?

A: Take x=2. g(2)=22=4. Take x=-2. g(-2)=(-2)2=4

Q: The following limit represents the derivative of a functionf at a point a. 5 tan 6. V3 f '(a) = =…

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Q: 2x - 3 Examine the function f(x):= x²+4 from the point of view of monotonicity and give its local…

A: This question can be solved using the concept of monotonicity and local extrema.

Q: f(x) – 10 • lim I – 1 = 6; • lim[g(x) + 2] = 5; • 3x < h(x) <r* + 2, for every x close to

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Q: Given f(x)= 6x –- 12 and g(x)=x – 4, find f(x)+g(x). Do not include spaces in your answer. Answer

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Q: Find the points of inflection of the function f(x)=x2lnx.

A: Inflection points are the points at which second derivative is zero. So differentiating f(x) with…

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.