Question

find an equation of the tangent line to the graph of f at the given point

f(x)=x^2 + 1 at point (2,5)

Answer 1

find the derivative of f(x)

Answer 2

Yes, the first thing to do is to find the derivative of f(x).
In this case, f'(x) = 2x
When x = 2, f'(x) = 4.

The slope should be +4, or positive 4.

If the slope is positive four and it is going through point (2,5), then

y = 4x - 3

This makes sense because if (2,5) is plugged back into the equation,
they are equal.

Here it is.

5 = 4*(2) - 3
5 = 8 - 3
5 = 5
CHECK

The answer is

y = 4x - 3.