Calculus Examples

Find the Critical Points 1/x
Step 1
Find the first derivative.
Tap for more steps...
Step 1.1
Find the first derivative.
Tap for more steps...
Step 1.1.1
Rewrite as .
Step 1.1.2
Differentiate using the Power Rule which states that is where .
Step 1.1.3
Rewrite the expression using the negative exponent rule .
Step 1.2
The first derivative of with respect to is .
Step 2
Set the first derivative equal to then solve the equation .
Tap for more steps...
Step 2.1
Set the first derivative equal to .
Step 2.2
Set the numerator equal to zero.
Step 2.3
Since , there are no solutions.
No solution
No solution
Step 3
Find the values where the derivative is undefined.
Tap for more steps...
Step 3.1
Set the denominator in equal to to find where the expression is undefined.
Step 3.2
Solve for .
Tap for more steps...
Step 3.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.2.2
Simplify .
Tap for more steps...
Step 3.2.2.1
Rewrite as .
Step 3.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.2.2.3
Plus or minus is .
Step 4
Evaluate at each value where the derivative is or undefined.
Tap for more steps...
Step 4.1
Evaluate at .
Tap for more steps...
Step 4.1.1
Substitute for .
Step 4.1.2
The expression contains a division by . The expression is undefined.
Undefined
Undefined
Undefined
Step 5
There are no values of in the domain of the original problem where the derivative is or undefined.
No critical points found