Question

Let f be the function defined by f(x) =x^4 -3x^2 +2
A)find the zeros of f
B)write an equation of the line tangent to the graph of f at the point where x=1
C) find the x coordinate of each point at which the line tangent to the graph of f is parallel to the line y=-2x+4

Answer 1

A) factor into (x^2-2)(x^2-1)
set each set of factors equal to zero and solve for x.

B) Take the derivative of the equation, plug in x=1 and solve...the answer is the slope (the slope of the tangent line at the point is the derivative of the eqn at that point)
Then, to get the y coordinate of the point @ x=1, plug in x into the original eqn and solve for y.
Then plug all of your solutions (the slope (m), x (given to you) , and y) into the eqn: y=mx + b
solve for b. Then plug m and b into y=mx +b

Answer 2

C) Parallel lines have the same slope. so find the values for which the derivative of f is equal to the slope of the new eqn. the slop of the new eqn is -2
so set the derivative (f'(x)) = -2 and solve for x.

Answer 3

So a) the zeros would be (radical2,0) and (1,0)
B) the equation of the line would be y=-2x+2

Answer 4

and I still don't understand how to do c