Jenelle Ramielcha Applications of Derivatives To be handed in Wednesday 6" April, 2022. 1. Find an equation of the tangent line to the graph of y' + y = 3x at the point where x = D find * dx 2. Chris and Jess had to find - for the function In (x -y) = >. a. Jess applied implicit differentiation to the problem in its original form. What did she get? b. Chris used exponentialion base e to eliminate the natural log, getting x - y = e", and then differentiated implicitly. What was his answer? K Jess and Chris then spent 15 minutes arguing about who was right. Who was? Justify your answer. 1 sentences. 3. Find the slope of the graph of (y -3) e* = x3 -11 at the point where y = 0. implit diffuinator 4. Find the slope of the graph of y = tan ( (x2 + >? )) at the point (. 1). 5. Find an equation of the tangent line to the graph of y* -3xy +4x =125 at the point in only neg the fourth quadrant where x = 2. 6. The graph of x2 + 6xy + 25y? =16 is an ellipse. Find the coordinates of the points where 1. find decide the ellipse has horizontal tangent lines. 2 SoluR ( x 74 7. Use logarithmic differentiation to find - if: loviclineres) Vx2 - 1exgot only = 0 outside y = when numer Aries x3 +x equells D 8. Determine the equation of the line tangent to the function f (x) = [(x + 1)+ + 1]in(x+1) at log its y-intercept. 1 =0 at -intercept 9. Determine the equation of the line tangent to the curve y = ex (x2 + 1)(me x at x =1. Find yualve first