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Undersök i vilka intervall som funktionen f(x) = x 3 -3x avtagande. In the exam, you would NOT have the graph below.

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Derivering av f(x) = x 3 – 3x ger f’(x) = 3x 2 – 3. When f’(x) = 0, x=-1 or x=1. This means the graph has either a max, a min or a ”terrasspunkt” ** at x=-1 or x=1. Look a the graph below. Note that, just to the left where x=-1, the gradient is +ve and just to the right of x=-1, the gradient is negative. Also, just to the left where x = 1, the gradient is negative and to the right it is positive. We draw a a table like this X-2012 F’(x)90-309 We can see that the graph ”avtagande” between -1 and 1 from the table. ** see the diagram at the top of page 136 in your book.

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Q2104a for vilka x-värden är funktionen avtagande? f(x) = 2x 2 – x 4 + 1 f’(x) = 4x – 4x 3 When f’(x) = 0, 4x – 4x 3 = 0 4x(1 – x 2 ) = 0 Therefore x = 0, -1 or 1 at max, min or ”terasspunkt”. Again draw a table X-2-0,500,512 F’(x)240-1,501,50-24 We can see that the graph ”avtagande” between -1 and 0 and when x is greater than or equal 1 from the table. See next slide.

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X-2-0,500,512 F’(x)240-1,501,50-24

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3.1 Inequalities and their graphs

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