Which is the equation of a line parallel to the line with equation y=3x-4
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Critical points is where the derivative (slope) is zero or does not exist. So to do this we have to find the derivative of our function:
So we apply chain rule:
=
Set our first derivative to zero and solve for x:
3(x^2 - 1) * 2x = 0
So we can see that (by plugging in) 0, -1 and 1 makes our solution true
So our critical value is x = 0, x = -1, x = 1
So we apply chain rule:
=
Set our first derivative to zero and solve for x:
3(x^2 - 1) * 2x = 0
So we can see that (by plugging in) 0, -1 and 1 makes our solution true
So our critical value is x = 0, x = -1, x = 1
Compute the necessary values/derivatives of at
:
Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial) at
by
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Another way of doing this would be to solve for the coefficients in
by expanding the right hand side and matching up terms with the same power of .