# Find the Local Maxima and Minima y=tan(x) Write as a function.
The derivative of with respect to is .
Find the second derivative of the function.
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
The derivative of with respect to is .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
To find the local maximum and minimum values of the function, set the derivative equal to and solve.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is equal to .
The range of secant is and . Since does not fall in this range, there is no solution.
No solution
Since there is no value of that makes the first derivative equal to , there are no local extrema.
No Local Extrema
Find the Local Maxima and Minima y=tan(x)     