Find the equation of the tangent line to x^2+5 at 2?

The tangent line to a curve, at a given point, represents
the derivative of the function of curve, at that
point.

We'll determine the 1st derivative of the
function:

f'(x) = 2x

But the
derivative of a function at a point is the slope of the tangent line at that
point:

m = f'(2) = 2*2 =
4

Now, we'll calculate the y coordinate of the point,
located on the given curve, whose x coordinate is 2.

f(2) =
4 + 5 = 9

We'll write the equation of a line that passes
through a point and it has a slope m.

y - y1 = m(x -
x1)

y - 9 = 4(x - 2)

y - 9 =
4x - 8

y = 4x +
1

The equation of the tangent line to the
curve y = x^2 + 5, at the point x = 2, is y = 4x +
1.