SOLUTION: 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?
(A) -6
(B) -1
(C) 1
(D) 4
(E) 6
Algebra ->
Test
-> SOLUTION: 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?
(A) -6
(B) -1
(C) 1
(D) 4
(E) 6
Log On
Question 243303: 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?
(A) -6
(B) -1
(C) 1
(D) 4
(E) 6 Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! 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?
(A) -6
(B) -1
(C) 1
(D) 4
(E) 6
----------
y' = 4x^3 + 2bx + 8 = 0 slope = 0
y'' = 12x^2 + 2b = 0 inflection
-----------------
2x^3 + bx + 4 = 0
6x^2 + b = 0
---------------
b = -6 (x = 1)
