Question

Find the average rate of change of the function from x=1 to x=2. f(x)=−14/x^2

Answer 1

Answer:

The average rate of change of the function from x=1 to x=2 will be: 10.5                

Step-by-step explanation:

Given the function

$f\left(x\right)=-\frac{14}{x^2}$

at x₁ = 1,

f(x₁) = f(1) =  -14/(1)² = -14/1 = -14

at x₂ = 2,

f(x₂) = f(2) = -14/(2)² = -14/(4) = -3.5

Using the formula to determine the average rate of change at which the total cost increases will be:

Average rate of change = [f(x₂) - f(x₁)] / [ x₂ - x₁]

                                        = [-3.5 - (-14)] / [2 - 1]

                                        = [-3.5 + 14] / [1]

                                        = 10.5 / 1

                                        = 10.5

Therefore, the average rate of change of the function from x=1 to x=2 will be: 10.5