Second Derivative Calculator

Step-by-Step Guide to Using the Second Derivative Calculator

Step 1: Select the Function Type

Begin by selecting the type of function you are working with. You will find a dropdown menu labeled Select Function Type. Click on it to choose from the available options, which are:

• Polynomial Function
• Exponential Function
• Trigonometric Function

This selection is required to ensure the calculator processes the function correctly.

Step 2: Enter the Coefficient (a)

Next, find the field labeled Coefficient (a). Enter the coefficient for your function in this input box. The input should adhere to the following constraints:

• The coefficient is required.
• It can range from -1000 to 1000.
• It should be entered with a precision of up to one decimal place (increments of 0.1 are allowed).

Step 3: Enter the Power (n)

After entering the coefficient, proceed to fill in the Power (n) field. This denotes the power to which the variable is raised in the function. Pay attention to the following guidelines while entering the power:

• This field is required.
• The power should be an integer between 0 and 10.

Step 4: Enter the x Value

Find the field labeled x Value, where you need to specify the x-value at which you want to evaluate the second derivative. Ensure that your input meets these criteria:

• The x value is required for computations.
• The acceptable range is between -100 and 100.
• Increments should be in steps of 0.1.

Step 5: View the Results

Finally, once all the required fields have been filled, the calculator will compute the results and display them in the following fields:

• First Derivative: Calculated using the formula: coefficient * power * pow(xValue, power - 1). The result will be shown with four decimal places.
• Second Derivative: Calculated using the formula: coefficient * power * (power - 1) * pow(xValue, power - 2). This result is also formatted to four decimal places.
• Concavity: Indicates whether the function is Concave Up, Concave Down, or Linear based on the sign of the second derivative. The result is prefixed with “Function is”.
• Inflection Point: Shows the x-value if an inflection point is present, which occurs when the second derivative is near zero (less than 0.0001). Otherwise, it will indicate ‘No inflection point at x’.

By following these steps, you can effectively use the Second Derivative Calculator to analyze the properties of your chosen function at a specific x-value.