CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

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


Solution


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

dydx=0 at x = 1 and = 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 = 2, then (a, b) =      -23,-16     .

Mathematics
RD Sharma XII Vol 1 (2019)
All

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
Same exercise questions
View More


similar_icon
People also searched for
View More



footer-image