Problem involving derivative and left-hand limit

In summary, a derivative is a mathematical concept that represents the rate of change of a function at a specific point and is calculated by finding the slope of a tangent line to the function at that point. A left-hand limit is the value that a function approaches as the input approaches a specific value from the left side. The derivative is related to a left-hand limit as it is a special type of limit called the instantaneous rate of change and is calculated by taking the limit of the slope of a secant line as the two points get closer and closer together. Derivatives and left-hand limits have various real-world applications and can be solved using techniques such as using the limit definition, power rule, product rule, and L'Hopital's rule
  • #1
Loopas
55
0
This is from an online homework that's due in an hour. This question has been bothering me all day and I'm convinced that there's a problem with the website.

It's asking for the expression that's used to find the left-hand limit of the derivative, f'(0).

It won't take 2x+6 as the answer... Am I missing something or is the website just screwed up?

I attached a picture of the problem. Help fast!
 

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  • #2
Do you remember the derivative of of $$x^n$$?
 
  • #3
Wouldn't that be n?
 

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is calculated by finding the slope of a tangent line to the function at that point.

What is a left-hand limit?

A left-hand limit is the value that a function approaches as the input approaches a specific value from the left side. It is denoted by the notation lim f(x) as x approaches a from the left.

How is a derivative related to a left-hand limit?

A derivative is a special type of limit called the instantaneous rate of change. It is calculated by taking the limit of the slope of a secant line as the two points get closer and closer together. In other words, the derivative is the left-hand limit of the function's slope at a specific point.

What are some real-world applications of derivatives and left-hand limits?

Derivatives and left-hand limits are used in various fields such as physics, economics, and engineering to model and analyze rates of change. For example, derivatives can be used to calculate velocity and acceleration, while left-hand limits can be used to determine the maximum or minimum value of a function.

What are some common techniques for solving problems involving derivatives and left-hand limits?

Some common techniques for solving problems involving derivatives and left-hand limits include using the limit definition of a derivative, using the power rule or product rule, and using L'Hopital's rule for indeterminate forms. It is also important to understand the properties and behaviors of different types of functions, such as polynomial, exponential, and trigonometric functions.

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