Is the logarithmic function , where an increasing or decreasing function, or neither? Explain using .
Question
Is the logarithmic function , where an increasing or decreasing function, or neither? Explain using .
Solution
The logarithmic function is an increasing function. Here's why:
-
The derivative of the logarithmic function is 1/x.
-
For all x > 0, the derivative 1/x is greater than 0.
-
According to the first derivative test, if the derivative of a function is greater than 0 for all x in its domain, then the function is increasing.
Therefore, the logarithmic function is an increasing function.
Similar Questions
Does the logarithmic function , where , have turning point(s)? Explain using .
_________ is a method that finds the derivative of the logarithm of the function rather than the original function*Logarithmic functionExponential functionLogarithmic DifferentiationNone of the choices
In mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation.The logarithm base 10 is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number e ≈ 2.718 as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base 2 and is frequently used in computer science.
The logarithmic function is the inverse of the Blank 1 Question 7 function.
What is the logarithmic form of:
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.