Write the equation of the tangent to the graph of the function y = x ^ 4 + x at the point with the abscissa x0 = 1.

The equation of the tangent to the graph of the function f (x) at the point x0 has the form:
y (x) = f ‘(x0) (x – x0) + f (x0);
f ‘(x) = 4x ^ 3 + 1;

Substitute the values x0 = 1 into the expressions for the function and its derivative:
f ‘(x0) = 4 1 + 1 = 5;
f (x0) = 1 + 1 = 2;
y (x) = 5 (x – 1) + 2 = 5x – 3.
Answer: y (x) = 5x – 3.