3.2 Polynomial functions and their graphs (15)

Question

The graph of a polynomial function is given.

P(x)= -(1/2)x^3 + (3/2)x - 1

The x y-coordinate plane is given. The curve enters the window in the second quadrant, goes down and right becoming less steep, crosses the x-axis at x = −2,changes direction at the point (−1, −2), goes up and right becoming more steep, passes through the point (0, −1), goes up and right becoming less steep, changes direction at the point (1, 0), goes down and right becoming more steep, and exits the window in the fourth quadrant.

(a) From the graph, find the x- and y-intercepts. (If an answer does not exist, enter DNE.)

x-intercept (smaller x-value) (x, y) = 

 x-intercept (larger x-value) (x, y) = 

y-intercept (x, y) = 

y-intercept (x, y) =  

(b)Find the coordinates of all local extrema. (If an answer does not exist, enter DNE.)

local minimum (x, y) = 

local maximum (x, y) = 

Answer 1

The local minimum is the lowest point of the main curve of your graph, while the local maximum is the highest point of the main curve of your graph. In this case, your local minimum is at (-1, -2) and your local maximum is at (1, 0).

Answer 2

1. Part A
2. smaller x int (-2, 0)
3. larger x intercept (1, 0)
4. y intercept (0, -1)
5. Part B
6. local min (-1, -2)
7. local max (1, 0)

Answer 3

x-intercepts are where it touches/crosses the x (horizontal) axis.

(-2,0)

(1,0)'

y-intercept is where it touches/crosses the y (vertical) axis.

(0,-1)