please show work for a b c

a) If s(t) = (12+ 3t ) sinh(t+1) , represents the position of an object, find the velocity function v(t) = s' (t). b) To optimize the speed of computer code, it is often helpful to approximate functions. like In a using polynomials. Find the linear approximation of the function f(x) = In x at a = 1 and use it to approximate In(1.3). c) Consider the function f(a ) = 4x3 - 2x + 4 on the domain a E [0, 2]. What does the Mean Value Theorem say about the derivative of this function? Find all points c E (0, 2) where the derivative assumes its mean value