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Lesson 6, Topic 2
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# Increasing & Decreasing functions

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The derivative of a function is positive over the range where it is increasing and negative where it is decreasing.

If y is increasing then, $$\frac{dy}{dx} \scriptsize > 0$$

If y is decreasing then, $$\frac{dy}{dx} \scriptsize < 0$$

Example:

find the range of values of for which the function

2x3 + 3x2 -12x + 5 is increasing

Solution:

Given y = 2x3 + 3x2 -12x + 5

then $$\frac{dy}{dx} = \scriptsize 6x^2 + 6x\; – 12$$

= 6(x2 + x – 2)

= 6(x + 2)(x – 1)

The function is increasing when, $$\frac{dy}{dx} \scriptsize > 0$$,

(x + 2)(x – 1) > 0

x > 1 or x < – 2

so the function is increasing when x > 1 or x < -2.

error: