Simplify the Differential Quotient | f(x) = 5x^2

In summary, To simplify the differential quotient, substitute the given function f(x) = 5x^2 into the formula (f(x+h)-f(x)) / h and calculate f(x+h) - f(x) by subtracting 5x^2 from the result of plugging in (x+h) for x in the original function. Then divide the result by h.
  • #1
Izekid
40
0
Simplify the differential qoutient like this (f(x+h)-f(x)) / h
and the qoute is f(x) = 5x^2

Please Help I don't know how to do this!
 
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  • #2
Didn't you forget a limit for h going to zero? Put in the function then...
 
  • #3
Izekid said:
Simplify the differential qoutient like this (f(x+h)-f(x)) / h
and the qoute is f(x) = 5x^2
Please Help I don't know how to do this!

You mean "difference quotient". You don't yet have a "differential" because, as TD said, you haven't taken the limit.

All we can say is "do what you are told!"

f(x)= 5x^2 so f(x+h)= 5(x+h)^2. Calculate that.
f(x+h)- f(x)= what you just did, minus 5x^2.

Last thing to do is divide by h.
 

1. What is the definition of the differential quotient?

The differential quotient is a mathematical concept used to find the instantaneous rate of change of a function at a specific point. It is also known as the derivative of the function and is represented by the symbol f'(x) or dy/dx.

2. How do you simplify the differential quotient for a given function?

To simplify the differential quotient, you need to follow the steps of the power rule. In this case, for the function f(x) = 5x^2, you would first multiply the coefficient 2 to the exponent, giving you 10x. Then, you would subtract 1 from the original exponent, giving you 1. So, the simplified differential quotient is f'(x) = 10x.

3. What does the value of the differential quotient represent?

The value of the differential quotient represents the slope of the tangent line at a specific point on the function. It tells us how much the function is changing at that particular point. A higher value indicates a steeper slope, while a lower value indicates a gentler slope.

4. How is the differential quotient used in real-life applications?

The differential quotient is used in various fields of science, such as physics, engineering, and economics, to analyze and model real-life phenomena. It is used to calculate rates of change, such as velocity, acceleration, and growth rates, which are essential in understanding the behavior of various systems and processes.

5. Can the differential quotient be used for any type of function?

Yes, the differential quotient can be applied to any type of function, including polynomial, exponential, trigonometric, and logarithmic functions. However, the process of simplifying the differential quotient may vary depending on the type of function. For example, different rules are used for exponential and trigonometric functions.

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