Find the point at which the following function has an inflection point: y = - 2x² + 3x + 6. A)3 B)1 C)2

Question

Quizplus · Accepted Answer

To find an inflection point, we need to find the second derivative of the function and set it equal to 0.

First, we find the first derivative: 
y' = -4x + 11eab9ea_e598_bf50_b53a_e59d687501bc_TB5481_11 + 3

Then, we find the second derivative: 
y'' = -4

Setting y'' equal to 0 shows that there are no inflection points in this function. However, if we wanted to find any points of maximum or minimum, we could set y' equal to 0 and solve for x: 
-4x + 11eab9ea_e598_bf50_b53a_e59d687501bc_TB5481_11 + 3 = 0 
-4x = -11eab9ea_e598_bf50_b53a_e59d687501bc_TB5481_11 - 3 
x = (11eab9ea_e598_bf50_b53a_e59d687501bc_TB5481_11 + 3)/4

This gives us the x-coordinate of a point of minimum. However, it is not an inflection point.

Find the Point at Which the Following Function Has an Inflection