given the function f defined by f(x) = 2x^3 - 3x^2 - 12x + 20?

Question

1) find the zeros of f.
2) write an equation of the line normal to the graph of f at x=0
3) find the x - and y-coordinates of all points on the graph of f where the line tangent to the graph is parallel to the X-axis.

Please help

Answer 1

f(x) = (2x + 5)(x - 2)^2
1) x = -5/2, 2
f'(x) = 6x^2 - 6x - 12
f'(0) = - 12
f(0) = 20
2) y = (1/12)x + 20
3) 6x^2 - 6x - 12 = 0
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1, 2
f(-1) = - 2 - 3 + 12 + 20
f(-1) = 27
f(2) = 16 - 12 - 24 + 20
f(2) = 0

Answer 2

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