Sections 5.3 and 5.4: Inverse Functions and the Exponential Function 1. Have we decided the tangent line problem is important yet? Consider the function f(x) = e3x+1 a. Find f'(x) b. Find the equation of the tangent line at x = 0 c. Sketch f(x) and the tangent line. Please use desmos to visually confirm your line is correct! d. Now, find the inverse function f-1(x). May want to plot on Desmos to confirm - is there symmetry about y = x? e. You should have found the point (0,2) on the graph of f. That means that (2,0) is a point on the graph of f-1. Find the derivative of the inverse at that point and compare: f'(0) = 2. Find the derivative of each function. a. f(x) = x^ex 3. Integrate. a e4x e4x + 1 (f-)'(2)= b. x4 g(x) = e2x + 1 b. dx x ex/2 dx