One Fine Day You Take a Hike Up a Mountain $y=3\left(x^{3}-12 x^{2}+48 x+36\right)$

question 10

Multiple Choice

One fine day you take a hike up a mountain path.Using your trusty map you have determined that the path is approximately in the shape of the curve $y=3\left(x^{3}-12 x^{2}+48 x+36\right)$ .Here y is the elevation in feet above sea level and x is the horizontal distance in miles you have traveled, but your map only shows the path for 7 miles, horizontal distance.Where on the path is a nice flat place to stop for a picnic?

• A)After 2 miles
• B)After 3 miles
• C)After 4 miles
• D)After 5 miles
• E)After 6 miles

---

Definitions:

Unvaccinated Person

An individual who has not received vaccination against specific diseases.

Macrophages

A type of white blood cell that engulfs and digests cellular debris, foreign substances, microbes, and cancer cells in a process called phagocytosis, playing an important role in the immune response.

Pathogens

Microorganisms that cause disease in their host, including bacteria, viruses, fungi, and parasites.

Graves' Disease

An autoimmune disorder that results in the overproduction of thyroid hormones (hyperthyroidism), characterized by symptoms such as enlarged thyroid, anxiety, hand tremor, heat sensitivity, weight loss, puffy eyes, and irregular heartbeat.