5. Find the average value of the function over the given interval, and all values of 1: in the interval for which the function equals its average value. 2 (a) rim) = w [1,3]. {b} f{m}=ain3:+coaa', [m31r]. 6. (a) Prove that ( f(t) at = f(h(z)n'(2) - f(g(x)g(2). [Hint: Rewrite the integral part using an antiderivative F of f. i.e, Use Fundamental Theorem of Calculus fa f(x) dx = F(b) - F(a).] (b) Find derivative of 13 $ 1+13 dt.7. The velocityr function t), in feet per second, is given as w} = 3t3 Qt + 34 for a particle moving along a straight line, where t is the time in seconds. Find the following: (a) The displacement over the time interval 1 it". t it". 5. {b} The total distance that the particle travels carer over the time internal 1 g t 5 5