3. (10 pts] Assume f and g are differentiable on their domains with h{x) = f [390). Suppose the equation of the line tangent to the graph of g at the point {4, 7) is y = 3x5 and the equation of the line tangent to the graph of f at (7,9) is y = 2x + 23. (a) {8 pts) Calculate 11(4) and 3114). (b) (2 ptsJ Determine an equation of the line tangent to the graph of h at the point [4,h(4]). Definition If y = f() is differentiable at a = a, then the approximationg function is given by the formula f ( x ) = f' la ) ( x-a) + f (a] y- fla) = fla) (x-a ) this is the tangent line tof at x = a and is called the linear approximation or tangent line approximation of f at a. The linearization of f at a is L ( x ) = f' la) ( x -a)+ fcaj The linearization is literally the tangent line fof at a.The Chain Rule If g is differentiable at a and f is differentiable at g(r), then the composite function F = fog defined by F(x) = f(g(x)) is differentiable at a and F' is given by the product F' (x ] = d ax ( fig ( x ) ) ) = f' (g ( x) ) . g' (x) In Leibniz notation, if y = f(u) and u = g(r) are both differentiable functions, then dy dy du du dxImplicit Differentiation Suppose we have an implicit equation of a curve, in terms of variables r and y, and we wish to find dy 1. Differentiate both sides of the equation with respect to x. 2. when differentiatingy with respect to x we must use chain rule. 3. solve for dy x using algebra Note your answer may have y in it