+76 A)
We can repeat the derivative operation: the second derivative \(f''\) is the derivative of \(f'\), the third derivative \(f'''\) is the derivative of \(f''\) , and so on. Find a function \(f\) such that \(f'\) and \(f''\) are not the function 0, but \(f'''\) is the constant function 0.
B)
Let \(f(x)\) and \(g(x)\) be functions with domain \((0,\infty)\). Suppose \(f(x)=x^2\) and the tangent line to \(f(x)\) at \(x=a\) is perpendicular to the tangent line to \(g(x)\) at \(x=a\) for all positive real numbers \(a\). Find all possible functions \(g(x).\)
