Find the angle between the tangent to the graph of the function y = x ^ 4-2x ^ 3 + 3 at the

Find the angle between the tangent to the graph of the function y = x ^ 4-2x ^ 3 + 3 at the point with the abscissa X0 = 1/2 and the Ox axis.

We calculate the derivative of this function in general form, we get:

y ‘(x) = 4 * x³ – 6 * x².

The value of this derivative at the point x = 1/2 will be the tangent of the angle of inclination of the tangent to the positive direction of the Ox axis, therefore:

y ‘(1/2) = 4 * (1/2) ³ – 6 * (1/2) ² = 1/2 – 3/2 = -1.

Therefore, the desired angle is arctan (-1) = -45 °.

Answer: The angle of the tangent is -45 °.