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- #1

- Feb 14, 2012

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Find $|f(0)|$.

- Thread starter anemone
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- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,522

Find $|f(0)|$.

up to down ) we shall have $f(1) = f(5)= f(6)$ and $f(2) = f(3) = f(7)$ and $f(1) \ne f(2)$.

For them to have values not meeting this criteria we shall have more humps .

As we are interested in absolute value we can choose $f(1) = - f(2) = 12$

As $f(1) = f(5)= f(6) = 12$ So we have $f(1) - 12 = f(5) - 12 = f(6) - 12 = 0$

So we can choose $f(x) = A(x-1)(x-5)(x-6) + 12 $ where A is a constant whose value we need to find

Putting $x=2$ we get $f(2) = A* 1 * (-3) *(-4) + 12 = 12A + 12 = - 12$ or A = -2

So $f(x) = -2(x-1)(x-5)(x-6) + 12$

Or $f(0) = -2 * (-1)(-5)(-6) + 12 = 72$

Or $\left | f(0) \right |= 72 $