Tyler began making regular deposits of a certain amount of money each month, m, starting August 14 The function F(m) = 5m + 400 models the amount of money in his account at any point in time after he started saving money. Assumìng Tyler made no withdrawals from the account after August 14, which of the following is not true? A) Tyler made onthly deposits of $5 per month B) Two months after he started saving, Tyler would have $410 in his account. C) After five months of saving, Tyler had $435 in his account. D) Tyler initially had $400 in his account before he began making regular monthly deposits.
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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