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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.

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Take the derivative, set it equal to 4, then solve for x.
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?
solve the resulting quadratic equation for \(x\)

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Other answers:

\[3x^2-4x+5=4\] \[3x^2-4x+1=0\] etc
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
@satellite73 is helping you the way I would've.

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