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SS3: MATHEMATICS - 2ND TERM

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  1. Matrices I | Week 1
    6 Topics
  2. Matrices II | Week 2
    1 Topic
    |
    1 Quiz
  3. Commercial Arithmetic | Week 3
    7 Topics
    |
    1 Quiz
  4. Coordinate Geometry | Week 4
    8 Topics
    |
    1 Quiz
  5. Differentiation of Algebraic Expressions | Week 5 & 6
    7 Topics
  6. Application of Differentiation | Week 7
    4 Topics
    |
    1 Quiz
  7. Integration | Week 8
    8 Topics
    |
    1 Quiz



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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.

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