Find the Critical Points f(x)=13x^4-78x^2

Problem

ƒ(x)=13*x4−78*x2

Solution

1. Find the derivative of the function using the power rule.

d(ƒ(x))/d(x)=52*x3−156*x

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

52*x3−156*x=0

3. Factor the expression by taking out the greatest common factor, which is 52*x

52*x*(x2−3)=0

4. Solve for x by setting each factor to zero.

52*x=0⇒x=0

x2−3=0⇒x2=3⇒x=±√(,3)

Final Answer

x=0,√(,3),−√(,3)

Want more problems? Check here!