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QUIZ_7NH_derivatives.doc Apr 6 22 N- NAME Due date: (last, first) Date the quiz was returned: Read first the files [1] 6C_Derivatives(OL).doc, [2] 8C_Derivatives of a power function.doc, [3] Problem set_4e (derivatives of power and polynomial functions)_sol.doc, [4] Problem set_5c (derivatives of power and polynomial functions)_sol.doc, [5] Problem set_6c (derivatives of product of two functions)_sol.doc, [6] Problem set_7c (derivatives of quotient of two functions)_sol.doc, [7] Problem set_8c (chain rule of differentiation)_sol.doc. Try to reproduce all results presented in these files by yourself. Then solve three problems below for your particular value of N. Find the equation of a tangent line y - F(x) = f'(x)" x - x) [l] to the graph of a given function F(x) at a specified point xı. Verify your results, check if the point (X1, F(x)) belongs to the line you found. To obtain some graphing evidence, use www.desmos.com/calculator to generate the graphs of both F(x) and y(x) (drag the whole graphing field with a mouse pointer and play with Zoom In and Zoom Out buttons [+], [-l in the desmos screen when necessary). In the text field of your answer message present the expression for the derivative F'(x), the values of F'(x1) and F(x), and the equation you obtained for a tangent line f(x)"g(x) 1. F(x) = (Nx + 1)*xFind the equation of a tangent line at the point x; = 1/4. Apply the product rule of differentiation for calculating the derivative of F'(x). Solution F'(x) = f(x)*g(x) = f(x)g(x) + g'(x)f(x) =