The feature y= x^4+bx^2+8x+1 has actually a horizontal tangent and a point of inflection for the very same value of x. Determine the worth of b.
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You are watching: The function y=x^4+bx^2+8x+1 has a horizontal tangent


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The function y= x^4 + b*x^2 + 8x+1. It has a horizontal tangent and also a allude of inflection for the same value of x.

The slope of a tangent at any type of point x is provided by the value of y" at that suggest. As the tangent is horizontal at the...


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The function y= x^4 + b*x^2 + 8x+1. It has a horizontal tangent and a suggest of inflection for the very same worth of x.

The slope of a tangent at any type of allude x is offered by the worth of y" at that point. As the tangent is horizontal at the forced value of x, y" = 0

=> 4x^3 + 2bx + 8 = 0

=> 2x^3 + bx + 4 = 0 ...(1)

Also, the feature has a point of inflection for the very same worth of x, y"" = 0

=> 12x^2 + 2b = 0

=> 6x^2 + b = 0 ...(2)

From (1) and (2) one real root of b is acquired and also it is equal to b = -6.

The compelled value of b = -6.

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