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

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)

RELATED QUESTIONS
Consider this function f(x) = x^3+ax^2+bx+c where a>=0, b>0 Over what intervals is f... (answered by robertb)

How do you determine the point (x,y) at which the graph of {{{ f(x) = (-8x)/sqrt(2x-1)... (answered by josgarithmetic)

Determine a quadratic function for y = ax^2+bx+c if its graph passes through the point... (answered by josmiceli)

Find the value of x that minimises y = 16x^2 + 1800/x for positive x. So first (answered by josgarithmetic)

Find all the points of inflection of the function f(x)=8x^2-2x^4 find point with... (answered by Alan3354,Earlsdon)

function: y= x^4-8x^3-16x+5 a. Identify the domain and range b. determine the x and... (answered by greenestamps)

Using the function y=(4x^2-8x+3)^4 find y' using the chain rule(extended power... (answered by jsmallt9)

The graph of a tangent function is given below. Find the equation of the graph in the... (answered by solver91311)

Find the equations of the tangent lines at all inflection points on the graph of:... (answered by Alan3354)