If The point P(1, 4) lies on the parabola y = x2 + 3x. What is the slope of the tangent to the parabola at P?
How do you determine what the tangent is in this case? Thanks
Let t denote the tangent to the parabola, $\displaystyle m_t$ the slope of the tangent.
1. $\displaystyle m_t = y'(1)$
From $\displaystyle y = x^2 + 3x$ you get $\displaystyle y' = 2x+3$ and therefore $\displaystyle m_t = 5$ at x = 1
2. Yo have the slope and a point of the line. Use the point-slope-formula to determine the equation of the line:
$\displaystyle y - 4 = 5(x-1)$ . Solve for y.