If f(x)=x^2+4x+6 what is the equation of the tangent to the curve when x=4?

Question

I can find the gradient of the tangent of the curve but i dont know what to do from there to get c (y=mx+c)

Answer 1

f(x)=x^2+4x+6
f'(x)=2x+4(differantiation to obtain the gradient of the curve)
x=4,f'(4)=2(4)+4(substitute x=4 to get the gradient)
=12
x=4,f(4)=4^2+4(4)+6(to find y)
=38
the point of the tangent is (4,38)
y-38=12(x-4)
y=12x-10

Answer 2

You have the gradient of the tangent, so you have m in y=mx + c.

By definition, the tangent touches the original curve at x=4 (and = f(4) ). That gives you a point on the tangent line, so you can calculate c.

Answer 3

f '(x)= 2x + 4
if x = 4, m = f '(4) = 12
so the equation of the tangent is :
y = 12 (x - 4) + f(4)
f(4)=16 + 16 + 6 = 38
y = 12x - 48 + 38 = 12x - 10