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- - **Line intersections**
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Line intersectionsEdit: Oops! This is in the wrong section, maybe it better fits in pre-calc/calc. I'll just walk through the question as it is asked in the book I'm studying. Excuse me for grammar errors. Suppose we have the following function: http://www.forkosh.com/mathtex.cgi?f...x%5E2+%2B+5%7D a) Calculate the extreme value of f(x) and give the range of f(x) So, we simply need to calculate f'(x) and set it to zero. Because I did answer a) correctly, I'll simply just get continue with posting f'(x) instead of deriving it step by step. http://www.forkosh.com/mathtex.cgi?f...%2B5%29%5E2%7D Now we need to set it to zero. http://www.forkosh.com/mathtex.cgi?f...=6x%5E2+%3D+30 Which will yield: http://www.forkosh.com/mathtex.cgi?f...%5Csqrt%7B5%7D Putting these values in the original equation will result in the extreme values: http://www.forkosh.com/mathtex.cgi?f...sqrt%7B5%7D%29 (minimum) and http://www.forkosh.com/mathtex.cgi?f...sqrt%7B5%7D%29 (maximum). The range of f(x) will thus be http://www.forkosh.com/mathtex.cgi?f...sqrt%7B5%7D%5D b) Calculate (algebraically) for which a the equation f(x) = ax has exactly one unique solution. So, from this point on I have absolutely no idea what to do. Can anyone help me out? c) Calculate (algebraically) for which p the equation f(x) = 2/3x + p has three solutions. I thought that if I could get some help on b I could try and solve b and c in this topic :^). |

You need to find where $f(x) = ax$. That is the same as finding where $$g(x) = f(x) - ax = 0$$ So, try solving that for $x$, and see what value of $a$ gives a single (possibly repeated) solution in the real numbers. |

Quote:
http://www.forkosh.com/mathtex.cgi?f...B5a-6%29+%3D+0 I get that I have to find where $f(x) = ax$, but I don't think I'll find it the way I'm trying right now. |

$\displaystyle \frac{6x}{x^2+5}=ax$ $\displaystyle 6=ax^2+5a$ $\displaystyle ax^2=6-5a=0\Rightarrow a=\frac65$ |

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