A) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1, 2). y = Correct: Your answer is correct. (b) At what points does this curve have horizontal tangents? (x, y) = -2 Incorrect: Your answer is incorrect. (smaller y-value) (x, y) = 2 Incorrect: Your answer is incorrect. (larger y-value)

Tangent at (1,2) has value . And (-2, 4) is the point of intersection of horizontal tangent.

Step-by-step explanation:

Given curve equation,

To find tangent at (x,y)=(1,2) and point of intersection of horizontal tangent, differentiate (1) withrespect to x we get,

At (1, 2), tangent line is,

To find point of intersection of horizontal tangent we have to do,

Thus,

At x=0, y=0

but snce,

at (0,0) there exist a vertical tangent. And,

At x=-2, y=4.

Thus (-2, 4) is the point of intersection of horizontal tangent.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: