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The average value of the function on the interval [-1, 6] is

Explanation:

The given

The average of a function is the height, 'h', of a rectangle with a width equivalent to the given interval and an area equivalent to the area of the function

The area under the graph of the function between the interval [-1, 6] consist of two right triangles and a rectangle and it is therefore given as follows;

The area. A = 1/2 × (0 - (-1)) × 2 + 2 × (6 - 0) + 1/2 × (4 - 2) × (6 - 4) = 15

The width of the rectangle, w = (6 - (-1)) = 7

w = 7

The area of the rectangle = h × w = A = 15

∴ The average value of the function, f = h = A/w = 15/7 =

Step-by-step explanation:

.632

step-by-step explanation:

6 * 1/10 = 3/5

3*0.01 = 0.03

3/5 + 0.03 = .63

2*0.002 = .002

.63 + 0.002 = .632

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)