Find the tangent of the angle of inclination of the tangent to the graph of the function y = x ^ 2

Find the tangent of the angle of inclination of the tangent to the graph of the function y = x ^ 2 at the point with the abscissa x0 = 1.

1. The tangent of the angle of inclination of the tangent with the abscissa axis is equal to the slope of the tangent, which, in turn, is equal to the value of the derivative of the function at the point of tangency:

tgφ = k = y ‘(x).

2. Find the derivative for a given function and calculate its value at a point with an abscissa x0 = 1:

y = x ^ 2;
y ‘= (x ^ 2)’ = 2x;
y ‘(x0) = y’ (1) = 2 * 1 = 2.
3. Angle tangent:

tg (φ0) = y ‘(x0) = 2.

Answer: 2.