Use calculus to determine whether the following utility functions imply risk aversion, risk neutrality or risk preference: a. U(W)equalsln(W) b. U(W)equalsUpper W Superscript 0.6 c. U(W)equalsUpper W Superscript 2.7 d. U(W)equals4W. The utility function, U(W)equalsln(W), implies ▼ risk aversion risk preferring risk neutrality because (as a function of W) StartFraction partial derivative squared Upper U (Upper W )Over partial derivative Upper W partial derivative Upper W EndFraction equals nothing. (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E. g., a superscript can be created with the ^ character.)

Demonstrate the proof of your new polynomial identity through an algebraic proof and a numerical proof in an engaging way! make it so the whole world wants to purchase your polynomial identity and can't imagine living without it! you must: label and display your new polynomial identity prove that it is true through an algebraic proof, identifying each step demonstrate that your polynomial identity works on numerical relationships create your own using the columns below. see what happens when different binomials or trinomials are combined. square one factor from column a and add it to one factor from column b to develop your own identity. column a column b (x − y) (x2 + 2xy + y2) (x + y) (x2 − 2xy + y2) (y + x) (ax + b) (y − x) (cy + d)

It is saturday morning and jeremy has discovered he has a leak coming from the water heater in his attic. since plumbers charge extra to come out on the weekends, jeremy is planning to use buckets to catch the dripping water. he places a bucket under the drip and steps outside to walk the dog. in half an hour the bucket is 1/5 of the way full. what is the rate at which the water is leaking per hour?

Graph the function =gx+2x3 and give its domain and range using interval notation.