Equations problem: tangent to curve x³-9x²+20x-8 at the point (1,4)

[Kitimbo]

Equations problem: tangent to curve x³-9x²+20x-8 at the point (1,4)

Find the equation of the tangent to curve x³-9x²+20x-8 at the point (1,4).At what points of the curve is the tangent parallel to the line 4x+y-3=0

Help me with the second part coz I can solve the first part

 

[HallsofIvy]

Since you have done "the first part", I presume that you realized that the derivative of y= x³-9x²+20x-8 is y'= 3x²- 18x+ 20. The line 4x+ y- 3= 0 can be written as y= 3- 4x so has slope -4. The tangent line to the cubic will be tangent to that line when 3x²- 18x+ 20= -4. Solve that quadratic equation.

 

[Kitimbo]

Thanks