Finding the Increasing/Decreasing Intervals

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The following table contains the supported operations and functions:. Enter the function of a variable:.

Enter an interval:. Required only for trigonometric functions.

Increasing and decreasing intervals

Differentiate using the Power Rule which states that is where. Since is constant with respect to , the derivative of with respect to is. Multiply by. Set the derivative equal to then solve for. Add to both sides of the equation. Divide each term by and simplify.

Increasing functions

Divide each term in by. Reduce the expression by cancelling the common factors. Cancel the common factor.

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    The complete solution is the result of both the positive and negative portions of the solution. Simplify the right side of the equation. Rewrite as. Pull terms out from under the radical, assuming positive real numbers. First, use the positive value of the to find the first solution.

    Next, use the negative value of the to find the second solution. The values which make the derivative equal to are. Split into separate intervals around the values that make the derivative or undefined.

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