# How do you find the average rate of change for the function #f(x) = x^3 - 4x^2# on the indicated intervals [0,10]?

The average rate of change of function

Keep in mind that a line's slope corresponds to the average rate of change.

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

To find the average rate of change of the function ( f(x) = x^3 - 4x^2 ) on the interval ([0,10]), 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. In this case, ( a = 0 ) and ( b = 10 ). Substituting these values into the formula:

[ \text{Average Rate of Change} = \frac{f(10) - f(0)}{10 - 0} ]

Calculate ( f(10) ) and ( f(0) ) by substituting ( x = 10 ) and ( x = 0 ) into the function ( f(x) = x^3 - 4x^2 ):

[ f(10) = (10)^3 - 4(10)^2 ] [ f(10) = 1000 - 400 = 600 ]

[ f(0) = (0)^3 - 4(0)^2 ] [ f(0) = 0 - 0 = 0 ]

Now substitute these values back into the formula:

[ \text{Average Rate of Change} = \frac{600 - 0}{10 - 0} = \frac{600}{10} = 60 ]

So, the average rate of change of the function ( f(x) = x^3 - 4x^2 ) on the interval ([0,10]) is 60.

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

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you use the derivative to find the slope of a curve at a point?
- What is the average rate of change of the function f given by #f(x)=x^4-5x# on the closed interval [0,3]?
- How do you find the points where the graph of the function # F(x)=x/(x^2+4)# has horizontal tangents and what is the equation?
- What is the instantaneous rate of change of #f(x)=3x+5# at #x=1#?
- How to calculate this? #int_0^piarcsin(cos^3x)dx#

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