Write the slope-intercept form of the equation of the line that is parallel to AB and passes through Point X. Show all work for full credit.

y=(-5/12)x+8

Step-by-step explanation:

find y=mx+b for line parallel to AB.

The line that is parallel will have the same slope as line AB:

the slope of line AB is

m=(8-3)/(-10-2)

  =5/-12

  =-5/12

Since the line going through X is parallel the vertical distance of the new line to AB is the same for all values of the domain(x-axis).

at x=-5 the point X has the y value of 10 which is 4 more than the y value for AB based on the graph.

To find the intercept b of the line going through X that is parallel to AB we just add 4 to the intercept of AB, which is 4 so

4+4=8

The point of inflection is calculated by equating the second derivative to zero and determining x from there.

f"(x) = -x²2xsinx² + cosx²(2x) = 0

2xcosx² - 2x³sinx² = 0
2x (cosx² - xsinx²) = 0

2x = 0   ⇒  x = 0
cosx² - xsinx² = 0   ⇒ x = 3.82 (if you use shift+solve in your scientific calculator)

Thus, the function only has 1 point of inflection and it is at x = 0.