Question 1 i) Let f(x) = ln(x) for x > 0, and g(x) = ln(-r) for...

   

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Question 1 i) Let f(x) = ln(x) for x > 0, and g(x) = ln(-r) for x <0. Compute f' and g'. i) If h(x) = In(x) for all x 0, what is h'? iii) For each positive real number c, define a(z) = In(er) for x>0. What is a'? Explain why your answer doesn't depend on c. Question 2 Consider the function f(x) = 4e-1 i) Find f(1) and f'(1). ii) Let f(1) =yo be your answer from part (i). Using the Inverse Function Theorem, find (f)'(yo). iii) Verify your answer to part (ii) by explicitly finding f and compute (f)'(yo). Question 3 i) Find all points on the curve x(x + y)=y where the tangent line is parallel to the x-axis. ii) Find all points on the curve (x + y) = y where the tangent line is parallel to the y-axis. Question 1 i) Let f(x) = ln(x) for x > 0, and g(x) = ln(-r) for x <0. Compute f' and g'. i) If h(x) = In(x) for all x 0, what is h'? iii) For each positive real number c, define a(z) = In(er) for x>0. What is a'? Explain why your answer doesn't depend on c. Question 2 Consider the function f(x) = 4e-1 i) Find f(1) and f'(1). ii) Let f(1) =yo be your answer from part (i). Using the Inverse Function Theorem, find (f)'(yo). iii) Verify your answer to part (ii) by explicitly finding f and compute (f)'(yo). Question 3 i) Find all points on the curve x(x + y)=y where the tangent line is parallel to the x-axis. ii) Find all points on the curve (x + y) = y where the tangent line is parallel to the y-axis.