Final answer:
The acute angle of intersection between two curves is found by taking the absolute value of the difference between their slopes, divided by 1 plus the product of their slopes, then taking the arctan of that value and converting it to degrees.
Step-by-step explanation:
To find the acute angle of intersection between the curves y = f(x) and y = g(x) at a point P, we need to consider the derivatives of the functions at that point. The derivatives give us the slopes of the tangent lines to the curves at the point of intersection. The angle of intersection, θ, between two lines with slopes m1 and m2 is given by the formula θ = arctan(|(m2 - m1) / (1 + m1 * m2)|). Convert θ to degrees by multiplying the radian measure by 180/π. If the angle found is obtuse, subtract it from 180 degrees to get the acute angle.