Consider the function () = 2 + 3. Find its average rate of change on the interval −1 ≤ ≤ 3.

See Explanation

Step-by-step explanation:

The function is not properly given. So, to solve this question I'll assume it is:

f(x) = x² + 3

Required

Calculate the average rate of change on −1 ≤ x ≤ 3.

[The average rate of change (R) is calculated using:]

R = (f(b) - f(a))/(b - a)

[Where]

a ≤ x ≤ b = −1 ≤ x ≤ 3.

[This means that]

a = -1

b = 3

[Solving f(b); We have]

f(x) = x² + 3

[Substitute b for x]

f(b) = b² + 3

[Substitute 3 for b]

f(3) = 3² + 3 = 9 + 3 = 12

[Solving f(a); We have]

f(x) = x² + 3

[Substitute a for x]

f(a) = a² + 3

[Substitute -1 for b]

f(-1) = (-1)² + 3 = 1 + 3 = 4

[So, the equation becomes]

R = (f(b) - f(a))/(b - a)

R = (12 - 4)/(3 - (-1)

R = 8/(3+1)

R = 8/4

R = 2

[Hence, the average rate of change is 2]

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