1530 G & H, Fall 2022 Assignment 7 Due by 11:59 pm on Monday, Nov 21 1. In the following questions y is defined implicitly as a function of z. Find du (a) 21ny + 10y - a + 21 = 0 (b) ze" - y? = 213 - ex-1 2. Suppose y is defined implicitly as function of a by the equation: ry +y' 2x. (a) Find y' (or at ) ") at the point (1. 1). (b) What is the equation of the straight line that is tangent to the curve (1,1). (Hint: you know the slope and a point on this straight line.) (c) What is the value of y" (or ,7 ) at the point (1, 1)? [Hint: remember is a function of z and that its derivative is $ 4.| 3. Consider the function: p(x) = In(2 + e"-3) when r > 0. (a) Does p(x) have an inverse function? (b) Find the inverse function of p(r). What is its slope? 4. Find ax dy by implicit differentiation: (a) 3y + x + 100 = 0 (b) y2 + x+ 100=0 (c) 3y + x2 + 100 =0 (d) y2 + 22+ 100=0 (e) y2 + xy + 22 + 100=0 N O O