Find The Critical Points F(x)=x^2 Natural Log Of X | Mathway

Enter a problem... Calculus Examples Popular Problems Calculus Find the Critical Points f(x)=x^2 natural log of x Step 1Find the first derivative.Tap for more steps...Step 1.1Find the first derivative.Tap for more steps...Step 1.1.1Differentiate using the Product Rule which states that is where and .Step 1.1.2The derivative of with respect to is .Step 1.1.3Differentiate using the Power Rule.Tap for more steps...Step 1.1.3.1Combine and .Step 1.1.3.2Cancel the common factor of and .Tap for more steps...Step 1.1.3.2.1Factor out of .Step 1.1.3.2.2Cancel the common factors.Tap for more steps...Step 1.1.3.2.2.1Raise to the power of .Step 1.1.3.2.2.2Factor out of .Step 1.1.3.2.2.3Cancel the common factor.Step 1.1.3.2.2.4Rewrite the expression.Step 1.1.3.2.2.5Divide by .Step 1.1.3.3Differentiate using the Power Rule which states that is where .Step 1.1.3.4Reorder terms.Step 1.2The first derivative of with respect to is .Step 2Set the first derivative equal to then solve the equation .Tap for more steps...Step 2.1Set the first derivative equal to .Step 2.2Subtract from both sides of the equation.Step 2.3Divide each term in by and simplify.Tap for more steps...Step 2.3.1Divide each term in by .Step 2.3.2Simplify the left side.Tap for more steps...Step 2.3.2.1Cancel the common factor of .Tap for more steps...Step 2.3.2.1.1Cancel the common factor.Step 2.3.2.1.2Rewrite the expression.Step 2.3.2.2Cancel the common factor of .Tap for more steps...Step 2.3.2.2.1Cancel the common factor.Step 2.3.2.2.2Divide by .Step 2.3.3Simplify the right side.Tap for more steps...Step 2.3.3.1Cancel the common factor of .Tap for more steps...Step 2.3.3.1.1Cancel the common factor.Step 2.3.3.1.2Rewrite the expression.Step 2.3.3.2Move the negative in front of the fraction.Step 2.4To solve for , rewrite the equation using properties of logarithms.Step 2.5Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .Step 2.6Solve for .Tap for more steps...Step 2.6.1Rewrite the equation as .Step 2.6.2Rewrite the expression using the negative exponent rule .Step 3Find the values where the derivative is undefined.Tap for more steps...Step 3.1Set the argument in less than or equal to to find where the expression is undefined.Step 3.2The equation is undefined where the denominator equals , the argument of a square root is less than , or the argument of a logarithm is less than or equal to .Step 4Evaluate at each value where the derivative is or undefined.Tap for more steps...Step 4.1Evaluate at .Tap for more steps...Step 4.1.1Substitute for .Step 4.1.2Simplify.Tap for more steps...Step 4.1.2.1Simplify the expression.Tap for more steps...Step 4.1.2.1.1Apply the product rule to .Step 4.1.2.1.2One to any power is one.Step 4.1.2.2Simplify the denominator.Tap for more steps...Step 4.1.2.2.1Multiply the exponents in .Tap for more steps...Step 4.1.2.2.1.1Apply the power rule and multiply exponents, .Step 4.1.2.2.1.2Cancel the common factor of .Tap for more steps...Step 4.1.2.2.1.2.1Cancel the common factor.Step 4.1.2.2.1.2.2Rewrite the expression.Step 4.1.2.2.2Simplify.Step 4.1.2.3Move to the numerator using the negative exponent rule .Step 4.1.2.4Expand by moving outside the logarithm.Step 4.1.2.5The natural logarithm of is .Step 4.1.2.6Multiply by .Step 4.1.2.7Multiply by .Step 4.1.2.8Move to the left of .Step 4.2Evaluate at .Tap for more steps...Step 4.2.1Substitute for .Step 4.2.2The natural logarithm of zero is undefined.UndefinedUndefinedStep 4.3List all of the points.Step 5

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