Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x) = x+ e-3X on the domain [-2,4]. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

Q: find the extrema (minimum and maximum) of f(x) = x2-1 on (-1,2). If none, explain why.

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Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 3 the point (2, 2.8).

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Q: Find the domain and range of  W=1/x+y

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Q: Your answer is partially correct. Find the coordinates of all points on the graph of y = 22 – x? at…

A: Given; y=22-x2

Q: Find Y = Coth 1 (x)

A: Given that y=coth-1x find dydx

Q: Write the equation for the curve that has slope of 2y/x for each point P(x,y) on it and passes…

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Q: Locate the stationary point of the following functions and determine their character. y= 1/2x^4 -…

A: Please see the below picture for detailed solution.

Q: Find a point on the curve y = x2 that is closest to the point (18; 0)

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Q: Determine the equation of the isogonal trajectories of the curves y = ce* if the angles of the…

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Q: Find the domain and range ofy = |2sin4x 21

A: We need to find domain and range of y=2 sin4x-12. The domain of a function is the set of input or…

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.