It’s a korean high school math problem Can you solve this?

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Lanca1
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View attachment 9200Hello, I,m korean high school student who likes mathematics. So I have made a math mock exam for KSAT, and this is a problem in the exam. It doesn’t need so long calculation but you can feel it a little difficult. (Sorry to my fool English performance. I’m not good at English)
 
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  • Printed math problem 28: f(x) is a quadratic with leading coefficient -1; g(x) = x^2 - 5x + 8 times e^x for x >= 0, and f(x) for x < 0; find the minimum of |g(t)| given g(t) < 0 and y = g(x)/(x - t) has only one extremum. [4 points]
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What do you mean by “highest order coefficient”? Do you mean the leading coefficient or the constant term?
 
Olinguito said:
What do you mean by “highest order coefficient”? Do you mean the leading coefficient or the constant term?


That means f(x) = -x^2 + ...