Derivative Plot
A derivative plotter typically plots a derivative function in blue and also plots the slope of the function on the graph shown in red (by computing the difference between each point in the original function, so it is not familiar with the formula for the derivative). In addition, you also have the option to plot another function in green below the computed slope. If the lines coincide with each other there are fair chances that you have found the derivative!
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Derivative Grapher Generator
Shown below is the graph of f(x).
The point marked "Slope of The Tangent Line contains a value ‘y’ which is the slope of the line tangent to the point "Drag Me"
Now, you can plot the graph of the derivative of this function by
1. Clicking on the "Begin Graphing the Derivative" button, then
2. Moving the point "Drag Me"
The graph of the f '(x) will be tracked down onto the screen.
When you click on "Stop Graphing The Derivative" the graph will withdraw.
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Change the equation of f(x) in the top left corner for the purpose of changing the function.
For each of the following functions, set a comparison of the graphs of the derivative of the functions to the common functions that you are known of. Can you determine the equation of the derivative functions?
Example:
Show that the function f(x) = x3– 2x² + 2x, x ∈ Q is increasing on Q.
Solution:
F(x) = x3 – 2x² + 2x
Upon differentiating both the sides, we obtain,
f'(x) = 3x² – 4x + 2 > 0 for each value of x
Hence, f is increasing on Q.
Derivative Visualization
Visualization of Derivative shows 4 different functions, which we can switch by pushing "Switch Function". It also consists of two points, F and M, and you can drag point M with the help of the slider. You can also display the tangent and chords using the derivative visualization.
Now let's play around until you understand the buttons
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Step 1: We want to identify the slope of the tangent line, which travels through point F on the function. Push the function "Show Tangent at F".
Step 2: We can now easily identify the slope between two points if we have their coordinates. Thus, if we have a point M, we can construct a chord across the two points, and identify the slope. Push "Show Chord Across F and M".
Objective: Now, we want to measure the slope of the tangent line at F, with the help of the chord through F and M.
Interactive Derivative Graph
Interactive Graph displaying Differentiation of a Polynomial Function.
In the following interactive derivative graph, you can explore how the slope of a curve changes as the changes the variable x.
Things to Do For Derivative Graph Calculator
Below we have taken the Derivatives of Polynomials.
In the left panel, you will notice the graph of the function of interest, and a triangle having a base 1 unit, stating the slope of the tangent. In the right panel is the graph of the 1st derivative (the dotted curve).
Take the help of the slider at the bottom in order to change the x-value. You can move the slider right or left (keeping the cursor within the light gray area) or you can also animate the points by holding down the "+" or "−" buttons on either side of the slider.
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Select another of the 2 examples in the pull-down menu.
The height of the right triangle implies the slope. It consists of a base of 1 unit.
Derivatives of 3 Functions
Below are the derivatives of the 3 functions:
1. Quadratic (parabola) y = x² - 10x -1
Derivative: dy/dx = 2x − 10
2. Cubic, y = 0.015x3 −0.25x² + 0.49x + 0.47.
Derivative: dy/dx = 0.045x² − 0.5x + 0.49
3. Quartic y = x4 − 1.5x3 − 6x² + 3.5x + 3.
Derivative: dy/dx = 4x3 − 4.5x² − 12x + 3.5.
FAQs on Derivative-Plotter
1. What is the Derivative of a Function?
Answer: In calculus, the derivative of a function of variable standards the sensitivity to change the output value in regards to a change in its input value. A derivative is a principal tool of calculus. This is to say, the derivative is the rate of change of one quantity in reference to another. With respect to functions, the rate of change of function is described as dy/dx = f(x) = y’.
For example, the derivative of the position of a moving object according to time-interval is the object’s velocity. It calculates the rapid change of the position of a person or object as time changes.
2. What are the Applications of Derivatives?
Answer: There are different applications of derivatives not only in maths but in real life too such as in fields like science, physics, engineering etc. There are derivatives of different functions, like, implicit functions, logarithm functions, trigonometric functions, etc. That being said, derivatives have different important applications in Mathematics that includes:
Rate of Change of a Quantity
Change of temperature
Rate of change of shapes and sizes of an object
Minimum and Maximum Values
Increasing and Decreasing Functions
Linear Approximations
Tangent and Normal to a Curve
Newton’s Method
3. What is the Rate of Change of a Quantity?
Answer: This is a usual and most significant application of derivative. For example, in order to check the rate of change of the volume of a cube in reference to its decreasing sides, we can apply the form of derivative dy/dx. Where dy indicates the rate of change of volume of cube and dx implies the change of sides of the cube.
