find the average rate of change of ( f(x)=-2x^{2}-x ) from ( x = 2 ) to ( x = 5 ).\nsimplify your answer as…

find the average rate of change of ( f(x)=-2x^{2}-x ) from ( x = 2 ) to ( x = 5 ).\nsimplify your answer as much as possible.

find the average rate of change of ( f(x)=-2x^{2}-x ) from ( x = 2 ) to ( x = 5 ).\nsimplify your answer as much as possible.

Answer

Answer:

-13

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) from (x=a) to (x = b) is (\frac{f(b)-f(a)}{b - a})

Step2: Find (f(2)) and (f(5))

  • For (x = 2): [ \begin{align*} f(2)&=-2\times(2)^{2}-2\ &=-2\times4 - 2\ &=-8-2\ &=-10 \end{align*} ]
  • For (x = 5): [ \begin{align*} f(5)&=-2\times(5)^{2}-5\ &=-2\times25-5\ &=-50 - 5\ &=-55 \end{align*} ]

Step3: Calculate the average rate of change

Here (a = 2), (b = 5), (f(a)=-10), (f(b)=-55) [ \begin{align*} \frac{f(5)-f(2)}{5 - 2}&=\frac{-55-(-10)}{5 - 2}\ &=\frac{-55 + 10}{3}\ &=\frac{-45}{3}\ &=-13 \end{align*} ]