Assume you have a savings bank account that initially contains Mo dollars. At the end of each year, you deposi constant amount of D dollars into the account. The savings account yields a 5% gains every year. onathan Jaimez-Me ), A 'w). (a) Compute, as function of Mo and D the dollar amount that you will have after one year (M2), and three years (M3): M1 = M2 (b) From the pattern above, write M, (dollar amount after n years) as a function of Mo and D, for general n using the sum (E) notation. Be clear about which terms are INSIDE the sum and which ones are OUTSIDE of the sum! i=0 21 5:06:10 PDT Mi3 09/Apr/2021 5e10 PDT Provided t 1151 So1 M Rewrite M, using the following partial geometric sum: M151 S21 MiniTesst3 09/A/2021 5:00-6:10 PD Provided to Jonathan" MiniTest3 09/Ar 202 Provided to Jona Jaimez-Me ed to PDT
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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