# Find the Local Maxima and Minima y=f'(x)

Rewrite the equation as a function of .
Since is constant with respect to , the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
To find the local maximum and minimum values of the function, set the derivative equal to and solve.
Since , the equation will always be true.
Always true
Evaluate the second derivative at . If the second derivative is positive, then this is a local minimum. If it is negative, then this is a local maximum.
Apply the first derivative test.
Split into separate intervals around the values that make the first derivative or undefined.
Substitute any number, such as , from the interval in the first derivative to check if the result is negative or positive.
Replace the variable with in the expression.
Substitute any number, such as , from the interval in the first derivative to check if the result is negative or positive.
Replace the variable with in the expression.