Calculus

First find the average value of the function by taking the integral of f(x) over the given Calculus AB/BC 1.) Given that f(x) and g(x) are f(x) = 8^x g(x)=64 ^(2x+1) determine the following a) f(x)g(x) b) state the domain of the product c) find the interval where the product is increasing A) f(x)g(x) = 8^x*64^(2x+1) = 512^(3x+1) B) Calculus 1. Use the intermediate value theorem to show that the equation 5x^3 = 3x has at least one real solution in the interval (0,1). 2. Use the Intermediate Value Theorem to show that the equation has at least one real solution in the interval (1,2).