# Math Help - Math help , paraboalas and tangents

1. ## Math help , paraboalas and tangents

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

2. Originally Posted by nosh

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, $m_t$ the slope of the tangent.

1. $m_t = y'(1)$

From $y = x^2 + 3x$ you get $y' = 2x+3$ and therefore $m_t = 5$ 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:

$y - 4 = 5(x-1)$ . Solve for y.