hi there, can someone please provide a full detailed solution to the following Calc 1 questions. thank you

Suppose f is a continuous function on the closed interval [4, 8] and the following values of f(a) are known: 4 5 6 8 f (z) -3 3 -4 -5 6 Of the following statements, select all that are always TRUE for a function with the above properties. [Hint: Try using the Intermediate Value Theorem!] DA. The equation f() = 0 has at least three solutions for a in the interval (4, 8). OB. The equation f(a) = 0 has at least one solution for a in the interval (4, 5). OC. The equation f(z) = 0 has no solutions for a in the interval (6, 7). OD. The equation f(a) = 0 has exactly one solution for a in the interval (7, 8). DE. The equation f() = 0 has exactly two solutions for a in the interval (4, 6).Suppose f is a one-to-one, differentiable function and its inverse function f is also differentiable. One can show, using implicit differentiation (do it!), that 1 ( f )' (20 ) = fi (f - 1 ( 20 ) ) Find (f-1)'(3) if f(2) = 3 and f'(2) = 2/5. (f-1)' (3 ) =Suppose that f( #) = -5 and f' (#) = 2, and let g(x) = f(x) sin a and h(x) COS f(a) Answer the following questions. 1. Find g'(7 / 4). Answer: g' (7/ 4) = 2. Find h' (7 / 4). Answer: h'(7 / 4) =\f