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- 1. a. Sketch the curve f(x) = x/(x-1)^2 b. Find the eh of the tangent and normal line of the function y^3+3xy+x^4=5 at the point (1,1). thank you.Suppose u and y are functions of x that are differentiable atx = 0 and that u(0) = 5, u(0) = -3, y(0) = -1, y(0) = 2.Find the values of the following derivatives at x = 0.24))Since the tangent of the curve y = x ^ 5 + ax - 3 at the point x = 1 is y = x -b, then b =?
- 6) If y = f(x) has slope −4 at x = 3, and y value 5 at x = 3, a) write the formula for the tangent line to f(x) at x=3: b) estimate f(3.02) from the tangent line: c) If f is known to be concave up (S), is f(3.02) bigger than or smaller than your answer in b)?Answer numbers 1,2 and 3 1.What is the derivative of f(x)=e8x+3? A.f′(x)=e8 B.f′(x)=8e C.f′(x)=8e8x+3 D.f′(x)=3e8x 2.What is the equation of the tangent line to the curve y=x^2−2x+1 at point (3,4)? A.y=−4x+8 B.y=2x−2 C.y=4x−8 D.y=x^3−2x^2+x 3.What are the critical points of f(x)=x^3−3x^2−3? A.(0,−3) and (2,−7) B.(0,3) and (2,7) C.(1,2) and (3,5) D.(0,2) and (2,6)Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x + 11. What are f(2) and f '(2)? If g(x) =[f(x)]2, find the linear approximation for g(x) at a = 2 .