Find the Critical Points y=4x^3-48x-5

Problem

y=4*x3−48*x−5

Solution

1. Find the derivative of the function with respect to x using the power rule.

d(y)/d(x)=12*x2−48

2. Set the derivative equal to zero to find the values of x where the slope of the tangent line is zero.

12*x2−48=0

3. Factor out the greatest common factor from the equation.

12*(x2−4)=0

4. Solve for x by factoring the difference of squares or by isolating the variable.

x2−4=0

x2=4

x=±2

5. Identify the critical points as the xvalues where the derivative is zero or undefined. Since the derivative is a polynomial, it is defined for all real numbers.

x=2,x=−2

Final Answer

x=2,−2

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