Use the following instructions to make a function f(x) and differentiate the function by using the appropriate derivative rule. A polynomial function of degree 4 with 5 terms. A two term function with x in square root and a cube root (can use coefficients and other exponents as well). A function with at least three terms and negative exponents The function is a product of a quadratic function and a cubic function. A composite function where the inner function is a quadratic and the outer function is a cube root function The function is a quotient of a quartic polynomial function in the numerator and a cubic function in the denominator.
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.
Use the following instructions to make a function f(x) and differentiate the function by using the appropriate derivative rule.
- A polynomial function of degree 4 with 5 terms.
- A two term function with x in square root and a cube root (can use coefficients and other exponents as well).
- A function with at least three terms and negative exponents
- The function is a product of a quadratic function and a cubic function.
- A composite function where the inner function is a quadratic and the outer function is a cube root function
- The function is a quotient of a quartic polynomial function in the numerator and a cubic function in the denominator.
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