Consider the polynomial f(x) = x + 4x^5. This function satisfies the horizontal line test and therefore has an inverse function f^(-1). In this question, we need to find the following values. For each value, either show your calculation or write one sentence to explain how you arrived at your answer: f(2), f(-111), f^(-1)(37).
b) Similar to Question 5 on the Module Part 1 content sheet, we will now use implicit differentiation to find the derivative of the inverse function f^(-1)(x). Start by setting y = f(x). This implies that x = f^(-1)(y) since inverse functions switch x and y values. Now use implicit differentiation on y + 4y^5 and solve for y'.
c) Lastly, use part b to find the slope of the line tangent to y = f(x) at x = 11. Remember that the slope is given by y'.