Find a formula for d2y /dx2 in terms of x and y if sin(xy) = x + y

Major Topic 2: Computing Derivatives
Compute the derivative each of the following functions, using any tools we have developed

(b) Find a formula for d2y /dx2 in terms of x and y if sin(xy) = x + y

Major Topic 3: Linear Approximation
(a) Give a formula for a linear approximation of f (x) = √x3 + 1 near the point a = 2.
(b) Use your answer in part (a) to estimate f (2.1).
(c) Write the equation for the tangent line to g(x) = x+2
x−5 at the point a = 6

M4: Extrema and Optimization
(a) Find the absolute extrema of g(x) = 3x4 − 2x3 − 3x2 + 5 on the interval [−1, 2], and
justify your claim that these are the absolute extrema.
(b) Find all the critical points of f (x) = 3
√x3 − 3x.

S5: Related Rates
A snowball is melting such that its surface area is decreasing at 1cm2/min. When the radius
is 8cm, how quickly is the radius decreasing?
(The surface area of a sphere of radius r is 4πr2.)
(a) Choose an equation to use for this problem, and explain why you chose that equation.
(b) Use calculus to answer the question. Make sure you answer with a complete sentence.