How would you find an equation of the line tangent to f(x) = 2x^2 - 4 at teh point (3, 14) ?
If f(2) = 3 and f(prime)(2) = -1, what would be the tangent line when x = 2?
first find the slope at the point, that is, find $\displaystyle f'(3)$
use that as your $\displaystyle m$ in the point-slope form
the tangent line will be given by: $\displaystyle y - y_1 = m(x - x_1)$
where $\displaystyle m$ is the slope and $\displaystyle (x_1,y_1)$ is a point the line passes through, here, this is namely $\displaystyle (3,14)$
here $\displaystyle m = -1$ and $\displaystyle (x_1,y_1) = (2,3)$ (do you see why?)If f(2) = 3 and f(prime)(2) = -1, what would be the tangent line when x = 2?
use the same method as above
Finding an equation tangent to that line at (3, 14) involves finding $\displaystyle f'(3) = 4(3) \rightarrow 12$ The values of the derivative function are the slope values at those points. You have the slope, and the x and y coordinates, so therefore you can solve for the equation of the line:
$\displaystyle y=mx+b$