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Increasing and Decreasing Functions

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How to find a range of values of x for an increasing or decreasing function?

The following diagrams show how to determine the range of values of x for an increasing or decreasing function. Scroll down the page for more examples and solutions on increasing or decreasing functions.

Increasing Decreasing Functions

Differentiation : Increasing & Decreasing Functions
This tutorial shows you how to find a range of values of x for an increasing or decreasing function.
Example:
Find the range of values of x for which y = x3 + 5x2 - 8x + 1 is increasing. Increasing Functions and Differentiation
Example:
For what values of x is y = 150x - 2x3 an increasing function?



Core 2 - Differentiation (1) - Increasing and Decreasing Functions Decreasing Functions : C2 Edexcel June 2010 Q3 Example:
y = x2 - k√x, where k is a constant.
(a) Find dy/dx
(b) Given that y is decreasing at x = 4, find the set of possible values of k. Increasing and Decreasing Functions and Stationary Points Stationary points, Increasing and Decreasing Functions Revision guide
Examples:
1. Prove that the curve y = x3 + 3x2 + 3x - 2 has only one stationary point. Show that the stationary point is a point of inflection.
2. Show that the curve y = 4x - x4 has only 1 stationary point. Determine the nature of this point.
3. Show that y = 1/3 x3 - 3x2 + 10x - 2 is an increasing function for all values of x.
4. For what values of x is y = x3 - 3x2 + 5 a decreasing function?

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