applications of derivatives

[vcmsandiego]

At how many values of x is the function f(x)=(4x^2-5x+1)(x-3) parallel to y=3x-9? I dont know how to start it.

 

[DrPhil]

At how many values of x is the function f(x)=(4x^2-5x+1)(x-3) parallel to y=3x-9? I dont know how to start it.

The slope of the function is the derivative. Differentiate to find f'(x), which will be a quadratic. The equation of the line is in slope-intercept form, so you can see what the slope is directly. Set f'(x) = m, and solve the quadratic - or at least determine how many solutions there are.

We need to see your work - show how far you can get.