Find the Critical Points 2-15x+9x^2-x^3

Problem

2−15*x+9*x2−x3

Solution

1. Define the function ƒ(x) based on the given expression.

ƒ(x)=2−15*x+9*x2−x3

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

d(ƒ(x))/d(x)=−15+18*x−3*x2

3. Set the derivative to zero to find the critical points, as critical points occur where ƒ(x)′=0 or is undefined.

−3*x2+18*x−15=0

4. Simplify the equation by dividing all terms by −3

x2−6*x+5=0

5. Factor the quadratic equation.

(x−5)*(x−1)=0

6. Solve for x by setting each factor equal to zero.

x−5=0⇒x=5

x−1=0⇒x=1

Final Answer

x=1,5

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