Find the critical point for f and then use the second derivative test to decide whether the critical point is a relative maximum or a relative minimum. f(x) = -x - 4x -6 The critical point for f is (2,-2). (Type an ordered pair.) Since the value of f" at the critical number is the relative extreme point is a relative Enter your answer in the answer box and then click Check Answer. All parts showing Clear All MacBook Pro 80 E3 esc F1 F2 DII F4 F7 F8 F10 @ € £ # 2$ & * 1 3 4 7 8. < O
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.
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