Find the equation of the tangent line to the parabola y=x^2+3x+2 at point P(1, 6).

In order to find the equation of the tangent line, first we have to find its slope. To do this, we take the first derivative of the function. In this particular case, we just need to apply the power rule (if y=x^n, dy/dx=nx^(n-1)) to each of the terms: y=x^2+3x+2 => dy/dx=2x+3 Having done that, in order to find the slope at the particular point we're looking at, we have to substitute for the value of x we are given, in this case x=1. If the slope of the tangent line at point P is m, m=2x1+3=5 Finally, in order to find the equation of the tangent line, we can use the straight line equation, y-y1=m(x-x1), where (x1, y1) are the coordinates of the point we're given. By substituting, we find: y-6=5(x-1) => y-6=5x-5 => y=5x+1 So, the equation of the tangent line is y=5x+1.

BA

Related Maths A Level answers

All answers ▸

How do I differentiate an algebraic expression? (e.g. y=3x^4 - 8x^3 - 3) [the ^ represents x being raised to a power]


Can you explain the product rule when differentiating?


Find dy/dx of 5x^2 + 2y^3 +8 =17.


The line l1 has equation 4y - 3x = 10. Line l2 passes through points (5, -1) and (-1, 8). Determine whether the lines l1 and l2 are parallel, perpendicular or neither.