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I posted a thread yesterday : Quadratic formula - math error

I've finally got an understand to it and can work out maximum/minimum ect but for the exam questions we're expected to give an answer like this : enter image description here

I've no idea what this means, if anyone could help me out in the most basic mathematic way possible. Cheers.

Community
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user119325
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2 Answers2

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The table simply means (from left to right):

  • When $x$ tends towards $-\infty$, $f(x)$ will tend towards $+\infty$
  • When $x$ is less than $9$, $f(x)$ will decrease
  • When $x = 9$, $f(x)$ has the value $0$, which is a local minimum of $f$
  • When $x$ is greater than $9$, $f(x)$ will increase
  • When $x$ tends towards $+\infty$, $f(x)$ will tend towards $+\infty$
Alex R.
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First of all $f$ must be a real valued function. In order to find min/max you need to study the graph of $f$ and see where it is monotone (increasing, decreasing). In order to do that usually you find the sign of the $f'$ and its roots. The roots of $f'$ are possible min/max of $f$. So you find the roots and draw a small table with rows $x, f(x),f'(x)$ and you mark the roots of $f'$ and the values of $x$ for which $f$ or $f'$ are not well defined. You put a + (-) sign where $f'$ is positive and this is where f is increasing (decreasing). If at a root of $f'$ there is a change of sign then you have a min/max. The arrows in the table mean decreasing and increasing respectively. You need to read some simple textbook describing how to find min/max in the way you want

Kal S.
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