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Question

If y=alogx+bx2+x has extreme values at x=1 and x=2. Find a and b.

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Solution

At extreme values, dydx at that point is zero
y=alogx+bx2x
x = - 1 is an extreme value
(dydx)x=1=0
dydx=9x+2bx+1
Now , (dydx)x=1,+91+2b(1)+1
a2b+1=0
a+2b=1 -- (1)
x = 2 is an extreme value
(dydx)x=2
(dydx)x=2=92+2b(2)+1
a2+4b+1=0
a+8b=1 _ (2)
subtracting equation (2) by (1), we get
6b = -2
b=13
substituting the above value in equation (1)
a+2(13)=1
a=53

1188589_1331793_ans_bb643202340c4f8291dac24a859f6426.png

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