Find all values of x where tangent lines to y= x^5 and y= x^6 are parallel. Give your answer in the form of a comma separated list. (Use symbolic notation and fractions where needed).

Answer 1

The tangent lines to the two functions are parallel only when their derivatives are the same.

So, 5x⁴ = 6x⁵.

5x⁴ - 6x⁵ = 0

x⁴(5 - 6x) = 0

x = 0, 5/6