Differentiate: g(x)=3×2+61+x2.

Find the points on the curve y=2×4-4×2 where the tangent line is horizontal.

Mrs. Thompson, an 82-year-old woman with limited mobility, is considering options for long-term care. Her family wants her to maintain as much independence as possible while receiving help with daily tasks like bathing, dressing, and meal preparation. Which type of long-term care setting best fits her needs?

Mrs. Patel, age 69, was diagnosed with pancreatic cancer. For months, she maintains her usual activities, attending social events and volunteering. However, over the last few weeks, her health declines sharply and rapidly. Which dying trajectory does Mrs. Patel’s experience most closely represent?

Mr. Ramirez, age 68, recently retired from his job as a high school teacher. Which aspect of his life would best reflect the Social Indicator Model?

Medicare, like Social Security, is a “pay-as-you-go” system, meaning that people paying into it now:

During a home visit, a healthcare professional notices multiple unexplained bruises and scars on Mr. Alvarez. He’s a 78-year-old patient who seems hesitant to explain how they occurred. Which important issue should always be considered in this situation?

A recent public health campaign is aimed at reducing preventable deaths among individuals aged 25-44 in the U.S. Which of the following interventions would be most effective in addressing the leading cause of death in this age group?

Dr. Wilson, a 66-year-old dentist, retires from his long-standing practice and moves to a new city to be closer to his adult children and grandchildren. This is an example of which retirement pattern?

Your grandfather seems increasingly distressed about attending your college graduation ceremony. He worries about being in large crowds, fears he might not be able to leave quickly if he feels overwhelmed, and has considered staying home to avoid the situation. Among adults 65 and older, which anxiety disorder is most prevalent and best explains his behavior?