Calculus Examples

Find the Critical Points 1/x
Step 1
Find the first derivative.
Find the first derivative.
Rewrite as .
Differentiate using the Power Rule which states that is where .
Rewrite the expression using the negative exponent rule .
The first derivative of with respect to is .
Step 2
Set the first derivative equal to then solve the equation .
Set the first derivative equal to .
Set the numerator equal to zero.
Since , there are no solutions.
No solution
No solution
Step 3
Find the values where the derivative is undefined.
Set the denominator in equal to to find where the expression is undefined.
Solve for .
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Plus or minus is .
Step 4
Evaluate at each value where the derivative is or undefined.
Evaluate at .
Substitute for .
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