Hi. Please answer the following question with detailed explanation

Find the following given that n} = 3, f'} = #5, gm} = 7.51mi 910) = '3. tan {r +y}'{U} =C] Kb: {r * mm E] m: {Ham} =C] Find a and b so that the function is both continuous and differentiable. mo ho The tangent line to y = f(@) at (-6, 2) passes through the point (0, -8). Compute the following. a.) f(-6) = b.) f'(-6) =Let f and g be functions such that f(9) = 21, f'(9) = 4, f(21) =17, f'(21) = -5. g(21) = -29, g'(21) = -10. g(17) = -27,and g'(17) = 53. (a) (go f)'(21) = (b) (fo f)'(9) =Use linear approximation to approximate v 16.3 as follows. Let f(x) = va. The equation of the tangent line to f(x) at * = 16 can be written in the form y = ma + b. Compute m and b. b Using this find the approximation for v/16.3. Answer:The acceleration due to gravity, g. is given by GM g = where M is the mass of the Earth, r is the distance from the center of the Earth, and G is the uniform gravitational constant. (a) Suppose that we increase from our distance from the center of the Earth by a distance Ar = @. Use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration: Ag ~ gx (Your answer will be a function of a and r.) (b) Is this change positive or negative? Ag is ? (Think about what this tells you about the acceleration due to gravity.) (c) What is the percentage change in g when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.28 km; assume the radius of the Earth is 6400 km)? percent change =