Page of 6 - ZOOM + Name: MATH 172 HW Week #3; 20 points; Due: July 13 at 11:59pm Summer 2022 Write detail work to the get full points. 1. Let f and g be differentiable functions for which the following information is known: f(2) = 5, g(2) = -3, f'(2) = -1/2, g'(2) = 2. a. Let h be the new function defined by the rule h(2) = 4f(x) + 39(z). Determine h(2) and h'(2). [1] b. Find an equation for the tangent line to y = h(r) at the point (2, h(2)). [1] c.If p(x) = f(x) . g(r) then calculate p'(2). [1]Page of 6 - ZOOM + b. Find an equation for the tangent line to y = h(r) at the point (2, h(2)). [1) c.If p(I) = f(x) . g(r) then calculate p'(2). = 12 then calculate d'(2). [1]