Question

Find the values of x for all points on the graph of f(x)=x^3-2x^2+5x-16 at which the slope of the tangent line is 4.

Answer 1

Take the derivative, set it equal to 4, then solve for x.

Answer 2

The derivative I found is 3x^2 -4x +5.
After that I make the whole thing equal to four?
Then I would subtract the 5 but after that what?

Answer 3

solve the resulting quadratic equation for \(x\)

Answer 4

\[3x^2-4x+5=4\]
\[3x^2-4x+1=0\] etc

Answer 5

i think you are lucky here in that this problem has been cooked so the quadratic factors, but you can always use the quadratic formula to solve any quadratic equation

Answer 6

@satellite73 is helping you the way I would've.