Let f(x) be the function defined by f(x) = 2x^3 - 3x^2 - 12x + 20.
a) Write an equation defined by the line normal to the graph of f(X) at x=0
b) Find the x and y coordinates of all points on all the graph of f(x) where the line tangent to the graph is parallel to the x-axis.
c) Sketch the graph of f with the line tangent to the point that you found from part b.

Question

Let f(x) be the function defined by f(x) = 2x^3 - 3x^2 - 12x + 20.
a) Write an equation defined by the line normal to the graph of f(X) at x=0
b) Find the x and y coordinates of all points on all the graph of f(x) where the line tangent to the graph is parallel to the x-axis.
c) Sketch the graph of f with the line tangent to the point that you found from part b.

anonymous · Answer

1) take the derivative
2) replace $x$ by 0 (  you will get -12)
3) normal line will have a slope that is the negative reciprocal $\frac{1}{12}$
4) use the point slope formula to find the equation of the line

anonymous · Answer

and how to do part b?