If true, show or explain why. If false provide a counterexample ( that is give a specific instance where the statement is not true).
a.) Let functions f and g along with their second derivatives exist for all x. If f and g are both concave up for all x, then f+g is concave up for all x.
b.) (f g)' is never equal to f' * g'
c.) The only functions with the fourth derivative y''''= sin x must be of the form y = sin x + c where c is a constant.
d.) The nth derivative of the function y = a^x is y to nth derivative = a^x(lna)^n