Directions: Determine what is asked in each problem as indicated by the blanks. 1. A school principal claims that the Grade 11 students in her high school have a mean score of 92. Null Hypothesis:. Alternative Hypothesis: Hai µ± 92 Parameter: Claim: mean score of 92 2. A medicine company has manufactured and claimed that their medicine pill contains an average of 14mg of active ingredient. Parameter: average Null Hypothesis:, Claim: average of 14mg Alternative Hypothesis: 3. A certain product produced by a manufacturing company is supposed to weigh at least 121bs. Null Hypothesis: Hoil > 121 Alternative Hypothesis: Parameter: Claim: weigh at least 12lbs_
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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