If the function `f(x)=x^4+b x^2+8x+1`
has a horizontal
tangent and a point of inflection for the same value of `x`
then the value of `b`
is equal to
`-1`
(b) 1
(c) 6 (d) `-6`
A
`-2`
B
`-6`
C
6
D
3
Text Solution
Verified by Experts
The correct Answer is:
B
According to the question we must have `f'(x)=0 and f''(x)=0` for the same `x=x_(0)` now `f'(x)=4x^(3)+2bx+8` `therefore" "f'(x_(0))=2[2x_(0)^(3)+bx_(0)+4]=0" (i)"` `"and "f''(x_(0))=2[6x_(0)^(2)+b]=0" (ii)"` From (ii) `b=-6x_(0)^(2)` Substituting this value of b in (i) `2x_(0)^(3)+(-6x_(0)^(2))+4=0 rArr 4x_(0)^(3)=4` `rArr" "x_(0)=1.` `rArr" "b=-6`
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