If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka

# Differential Calculus Calculators I greet you this day,
I wrote the codes for some of the calculators using JavaScript, a client-side scripting language.
The Wolfram Alpha widgets (many thanks to the developers) were used for some calculators.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.
If you are my student, please do not contact me here. Contact me via the school's system.
Thank you for visiting.

Samuel Dominic Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S

## Applications of Derivatives

### Extrema

Use only $x$
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Determine the extrema (maxima and minima) of a function within a domain.
(2.) Determine the extrema (maxima and minima) of a function without bounds. In this case, please specify the bounds are $-\infty$ and $\infty$.
(3.) Graph the function and indicate the extrema on the graph.

(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed. Do not include $y = \;\;the\;\;function$
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the appropriate textbox of the calculator.
(5.) Type the domain of the function accordingly in the appropriate textbox of the calculator.
(6.) Click the "Submit" button.
(7.) Check to make sure that it is the correct function and domain that you typed.
(8.) Review the answers. At least one of the answers is probably what you need.

• Using the Extrema Calculator
• Type: $-\infty$ as -\infty
• Type: $\infty$ as \infty
• Type: $7$ as 7
• Type: $4x + 3$ as 4 * x + 3 * x
• Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
• Type: $4x^3 - 5x^2 + 4$ as 4 * x^2 - 5 * x^2 + 4
• Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
• Type: $|-7 - 5x|$ as |-7 - 5x|
• Type: $12e^{-3x}$ as 12 * e^(-3 * x)
• Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
• Type: $(\log x)^5$ as (log x)^5
• Type: $\sec^2 x$ as sec^2 x
• Type: $\cos hx$ as cos hx
• Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
• Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Function:

### Optimization

Use only $x$ and $y$
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Determine the global/absolute extrema (global maximum and global minimum) and local/relative extrema (relative maximum and relative minimum) of a function (as applicable) within several constraints.
(2.) Graph three-dimensional plot (3D plot) and a contour plot of the objective funtion within the constraints.
(2.) Indicate the extrema on those plots.

(1.) Type the objective function in the first textbox (the bigger textbox).
(2.) Type it according to the examples I listed. Do not include $y = \;\;the\;\;function$
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the appropriate textbox of the calculator.
(5.) Type the constraints in the second textbox (the bigger textbox).
Separate each constraint with a comma. Do not put a comma or period at the end.
(6.) Copy and paste the constraints you typed, into the appropriate textbox of the calculator.
(7.) Click the "Optimize" button.
(8.) Check to make sure that it is the correct function and domain that you typed.
(9.) Review the answers. At least one of the answers is probably what you need.

• Using the Optimization Calculator
• Type: $-\infty$ as -\infty
• Type: $\infty$ as \infty
• Type: $7$ as 7
• Type: $4x + 3$ as 4 * x + 3 * x
• Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
• Type: $4x^3 - 5x^2 + 4$ as 4 * x^2 - 5 * x^2 + 4
• Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
• Type: $|-7 - 5x|$ as |-7 - 5x|
• Type: $12e^{-3x}$ as 12 * e^(-3 * x)
• Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
• Type: $(\log x)^5$ as (log x)^5
• Type: $\sec^2 x$ as sec^2 x
• Type: $\cos hx$ as cos hx
• Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
• Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Objective Function:

Constraints: