# How do you find the average rate of change of # f(x)=x^2-6x+8# over the interval [4,9]?

7

in order to determine the average rate of change between the two usage points.

The difference in change from (4,0) to (9,35) at an average rate is

This indicates that between (4,0) and (9,35), the average slope of all the lines tangent to the graph of f(x) is 7.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the average rate of change of ( f(x) = x^2 - 6x + 8 ) over the interval ([4,9]), you can use the formula:

[ \text{Average rate of change} = \frac{f(b) - f(a)}{b - a} ]

where (a) and (b) are the endpoints of the interval.

Plugging in the values:

(a = 4), (b = 9)

(f(4) = (4)^2 - 6(4) + 8 = 8)

(f(9) = (9)^2 - 6(9) + 8 = 35)

[ \text{Average rate of change} = \frac{35 - 8}{9 - 4} = \frac{27}{5} = 5.4 ]

So, the average rate of change of ( f(x) ) over the interval ([4,9]) is (5.4).

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you find the equation of a line tangent to the function #y=2-sqrtx# at (4,0)?
- How do you use the limit definition to find the derivative of #2sqrtx-1/(2sqrtx)#?
- How do you find the value #a > 0# such that the tangent line to #f(x) = x^2 * e^-x# passes through the origin #(0,0)#?
- What is the equation of the line tangent to #f(x)=cosx-sinx# at #x=pi/3#?
- What is an equation of the line tangent to the graph of #y=cos(2x)# at #x=pi/4#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7