tangent line equations

Question

The line y = b + mx is tangent to the graph of f at x = 7. Given that f( 7) = 5, the derivative f'( 7) = 4, and f"( 7) = 4, find m and b.

Answer 1

These problems are the same as finding the equation of a line at a point and given a slope:

y - y_p = m(x - x_p) where m is slope and the point in question is (x_p,y_p)

In this case x_p = 7 y_p = f(7) = 5 and m = f'(7) = 4

You can rearrange to solve for the y intercept, b or you can just plug in x = 0 and solve for y.

Please consider a tutor.

Answer 2