All Calculus 1 Resources
Example Questions
Example Question #1 : Rate Of Change
Determine the average rate of change of the function from the interval .
Write the formula to determine average rate of change.
Substitute the values and solve for the average rate of change.
Example Question #1 : Rate Of Change
Find the rate of change of a function from to .
Write the formula for the average rate of change from the interval .
Solve for and .
Substitute the known values into the formula and solve.
Example Question #1 : How To Find Rate Of Change
Suppose the rate of a square is increasing at a constant rate of meters per second. Find the area's rate of change in terms of the square's perimeter.
Since the question is asking for the rate of change in terms of the perimeter, write the formula for the perimeter of the square and differentiate it with the respect to time.
The question asks in terms of the perimeter. Isolate the term by dividing four on both sides.
Write the given rate in mathematical terms and substitute this value into .
Write the area of the square and substitute the side.
Since the area is changing with time, take the derivative of the area with respect to time.
Substitute the value of .
Example Question #2911 : Calculus
Determine the point on the function that is not changing:
In order to determine where the function is not changing, it is necessary to take the derivative and set the slope equal to zero. This will provide information on where the curve is not changing. Once we find the x value that gives the derivative a slope of zero, we can substitute the x-value back into the original function to obtain the point.
Substitute this value back to the original equation to solve for .
The point where the function is not changing is .
Example Question #1 : Rate Of Change
For the function , what is the average rate of change from to ?
Write the formula for average rate of change.
Determine the values of and .
Substitute the known values.
Example Question #2 : Rate Of Change
Find the rate of change of a function from to .
We can solve by utilizing the formula for the average rate of change: Solving for at our given points:
Plugging our values into the average rate of change formula, we get:
Example Question #2 : Rate Of Change
Find the rate of change of a function from to
We can solve by utilizing the formula for the average rate of change: . Solving for at our given points:
Plugging our values into the average rate of change formula, we get:
Example Question #3 : Rate Of Change
Find the rate of change of a function from to .
We can solve by utilizing the formula for the average rate of change: . Solving for at our given points:
Plugging our values into the average rate of change formula, we get:
Example Question #1 : Rate Of Change
Find the rate of change of a function from to .
We can solve by utilizing the formula for the average rate of change:
.
Solving for at our given points:
Plugging our values into the average rate of change formula, we get:
Example Question #1 : How To Find Rate Of Change
Find the rate of change of a function from to .
We can solve by utilizing the formula for the average rate of change:
.
Solving for at our given points:
Plugging our values into the average rate of change formula, we get:
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