Find the Critical Points f(x)=-x^2+8x-3

Problem

ƒ(x)=−x2+8*x−3

Solution

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

d(ƒ(x))/d(x)=−2*x+8

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

−2*x+8=0

3. Solve for x by isolating the variable on one side of the equation.

−2*x=−8

x=4

4. Verify the domain of the original function to ensure the value is a valid critical point. Since ƒ(x) is a polynomial, it is defined for all real numbers.

x=4

Final Answer

x=4

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