Find all value(s) of x

Question

Find all value(s) of x at which the tangent lines to the graph of f(x)= arctan(4x) are perpendicular to the line which passes through (0, 1) and (2, 0).

Answer 1

Slope m of line passing this points m = (0 - 1)/(2 - 0) = -1/2.

Slope of perpendicular line (tangent line) f'(x) = 2 or 4/(1 + 16x²) = 2; 4 = 2 + 32x²; x² = 1/16; x = ±1/4