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For the function y = m log x + n x² + x, if the extreme points occur at x = 1 and x = 2, then the value of 2m + 10n is:

1. 1
2. −4
3. −2
4. −3

Correct answer: −3

Solution

y'=m/x+2nx+1. Setting y'=0 at x=1 and x=2 gives m+2n+1=0 and m/2+4n+1=0, solving m=-2/3, n=-1/6. Then 2m+10n = -4/3 - 5/3 = -3.

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