Calculus Examples

Find the Absolute Max and Min over the Interval
,
Find the first derivative.
Tap for more steps...
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Evaluate .
Tap for more steps...
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Set the first derivative equal to zero.
Solve to find the critical points.
Tap for more steps...
Factor out of .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
Tap for more steps...
Divide each term in by .
Reduce the expression by cancelling the common factors.
Tap for more steps...
Cancel the common factor.
Divide by .
Divide by .
Set equal to and solve for .
Tap for more steps...
Set the factor equal to .
Add to both sides of the equation.
The solution is the result of and .
Use the endpoints and all critical points on the interval to test for any absolute extrema over the given interval.
Evaluate the function at .
Tap for more steps...
Simplify each term.
Tap for more steps...
Remove parentheses.
Raising to any positive power yields .
Remove parentheses.
Raising to any positive power yields .
Multiply by .
Simplify by adding zeros.
Tap for more steps...
Add and .
Subtract from .
Evaluate the function at .
Tap for more steps...
Simplify each term.
Tap for more steps...
Remove parentheses.
Raise to the power of .
Remove parentheses.
Raise to the power of .
Multiply by .
Simplify by subtracting numbers.
Tap for more steps...
Subtract from .
Subtract from .
Evaluate the function at .
Tap for more steps...
Simplify each term.
Tap for more steps...
Raise to the power of .
Multiply by by adding the exponents.
Tap for more steps...
Combine and
Tap for more steps...
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Raise to the power of .
Simplify by subtracting numbers.
Tap for more steps...
Subtract from .
Subtract from .
Evaluate the function at .
Tap for more steps...
Simplify each term.
Tap for more steps...
Remove parentheses.
Raise to the power of .
Remove parentheses.
Raise to the power of .
Multiply by .
Simplify by subtracting numbers.
Tap for more steps...
Subtract from .
Subtract from .
Compare the values found for each value of in order to determine the absolute maximum and minimum over the given interval. The maximum will occur at the highest value and the minimum will occur at the lowest value.
Absolute Maximum:
Absolute Minimum:
Enter YOUR Problem
Mathway requires javascript and a modern browser.
Cookies & Privacy
This website uses cookies to ensure you get the best experience on our website.
More Information