Find the Critical Points y=4x^3-48x-1

Problem

y=4*x3−48*x−1

Solution

1. Find the derivative of the function with respect to x to determine the rate of change.

d(y)/d(x)=12*x2−48

2. Set the derivative to zero because critical points occur where the first derivative is zero or undefined.

12*x2−48=0

3. Factor out the greatest common factor to simplify the quadratic 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. Find the y-coordinates by substituting the x values back into the original function y=4*x3−48*x−1

y(2)=4*(2)3−48*(2)−1=32−96−1=−65

y*(−2)=4*(−2)3−48*(−2)−1=−32+96−1=63

Final Answer

(2,−65),(−2,63)

Want more problems? Check here!