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Question

If y = a log x + bx2 + x has its extreme values at x = 1 and x = 2, then (a, b) = ____________________.

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Solution


It is given that, y=alogx+bx2+x has its extreme values at x = 1 and x = 2.

dydx=0 at x = 1 and x = 2

y=alogx+bx2+x

Differentiating both sides with respect to x, we get

dydx=ax+2bx+1

Now,

dydxx=1=0

a+2b+1=0

a+2b=-1 .....1

Also,

dydxx=2=0

a2+4b+1=0

a+8b=-2 .....2

Subtracting (1) from (2), we get

6b = −1

b=-16

Putting b=-16 in (1), we get

a+2×-16=-1

a=-1+13=-23

Thus, the values of a and b are -23 and -16, respectively.

Hence, the ordered pair (a, b) is -23,-16.


If y = alogx + bx2 + x has its extreme values at x = 1 and x = 2, then (a, b) = -23,-16 .

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