- #1
dbag123
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- Homework Statement
- Draw a derivative of a function
- Relevant Equations
- -
Red line being the function and blue an approximation of the derivative. Does it look right?
Almost. I think at the beginning (around ##x=\frac{1}{2}##) the curve gets steeper for a moment before it flattens again, so the derivative there should first increase a bit. I think at ##3/5## is an inflection point.dbag123 said:Problem Statement: Draw a derivative of a function
Relevant Equations: -
View attachment 243898
Red line being the function and blue an approximation of the derivative. Does it look right?
Thank youfresh_42 said:Almost. I think at the beginning (around ##x=\frac{1}{2}##) the curve gets steeper for a moment before it flattens again, so the derivative there should first increase a bit. I think at ##3/5## is an inflection point.
You were to sketch the derivative, ƒ'(x), of the function, the derivative being the slope of the line tangent todbag123 said:Problem Statement: Draw a derivative of a function
Relevant Equations: -
(Image removed for this reply)
Red line being the function and blue an approximation of the derivative. Does it look right?
A derivative of a function is a mathematical concept that represents the rate of change of the function at a specific point. It is essentially the slope of the function at that point.
A derivative can be calculated using the limit definition, which involves finding the slope of the function at two points that are very close together. It can also be calculated using rules such as the power rule, product rule, and chain rule.
The purpose of finding a derivative of a function is to understand the behavior of the function. It can help determine the maximum and minimum points, the direction of the function, and the rate of change at a specific point.
Yes, a derivative of a function can be negative. This indicates that the function is decreasing at that point.
Yes, derivatives have many real-world applications, such as in physics to calculate velocity and acceleration, in economics to determine marginal cost and revenue, and in engineering to optimize designs and processes.