Finding b in a Function with Horizontal Tangent and Point of Inflection

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In summary, the function y=x^4+bx^2+8x+1 has both a horizontal tangent and a point of inflection for the same value of x. To find the value of b, one must set the second derivative of the function to zero. The possible values for b are -6, -1, 1, 4, and 6.
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hamburgler
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I'm doing a calc BC practice exam and I found this question that stumps me to the max:

The function y=x^4+bx^2+8x+1 has a horizontal tangent and a point of inflection for the same value of x. What must be the value of b?


I know that points of inflection are found from the second derivative and setting that function to zero, however the 'b' value really throws me off :yuck:

Oh btw here are the mc answers.

a) -6 b)-1 c) 1 d) 4 e) 6
 
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  • #2
under what conditions does the function have a hotizontal tangent
Under what conditions does the function have a point of inflection
once you know that it should be easy to see when both occur
you will also see what b must be
 

1. What is the format of the Calc BC Exam Question?

The Calc BC Exam Question follows a multiple-choice and free-response format. The multiple-choice section includes 45 questions, with 1 hour and 45 minutes to complete. The free-response section includes 6 questions, with 1 hour and 30 minutes to complete.

2. What topics are covered on the Calc BC Exam Question?

The Calc BC Exam Question covers a wide range of topics, including limits, derivatives, integrals, differential equations, applications of integrals, and series. It also includes topics from Calculus AB, such as functions, graphs, and basic differentiation and integration.

3. How is the Calc BC Exam Question graded?

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4. Are calculators allowed on the Calc BC Exam Question?

Yes, calculators are allowed on both the multiple-choice and free-response sections of the Calc BC Exam Question. However, only specific models are permitted, so it is important to check the College Board's guidelines before the exam.

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