Question

the graph f(x)=x^3-6x^2+4x-3 crosses the x-axis at one point. What is the slope of the graph at that point. Round your answer to three decimal place.

Answer 1

We take the derivative of x^3 -6x^2 + 4x -3 which is

3x^2 -12x +4 = 0

Then we have to calculate the equation's value when y = 0 which in this case occurs when x = 5.3579 (the equation's only real root).

3*5.3579 * 5.3579 -12*5.3579 +4 = 25.82647723

which rounds to 25.826

Explanation: