calculus help please?

Question

f (x) = x^2 + 1

find the equation of the tangent line at the point (2, 5)
the answer is y = 4x - 3
how do i get to this answer? please show steps and explain them as much as possible. thanks

Answer 1

The derivative of the function is the gradient of the tangent line.

f'(x) = 2x by the power rule: d/dx x^n = nx^(n-1).
So f'(2) = 4.
So the tangent line has gradient 4 and passes through (2, 5). So it must have equation y-5 = 4(x-2)
<=> y = 4x - 3.