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

A convenient way to find the zeros of   is by factoring.

a) The equation,

can be rewritten as,

We can think of this equation as a quadratic equation in  , with .

Observe that .

We find two factors of 2 that adds up to . These are, .

Now let us split the middle term. to obtain;

We can factor to get,

We factor further to obtain;

Hence the zeroes of are;

b) To find the line tangent, we must first, find the slope using differentiation. That is,

At ,

Also, we need to determine the value at . That is;

Now we can use the slope and the point to write ythe equation of the line tangent.

c)

If the line tangent is parallel to the line , then

Since parallel lines have the same slope.

Hence the x-coordinates are,

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x