Calculus Project

What is the derivative?

• A
• B
• C
• D

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Answer the following:

• B
• C
• D
• E

Consider the differential equation dy/dx = x + 2y for which g(x) is the solution.  Which of the following statements is true if the particular solution contains (0,-1)

• g(x) is increasing and concave up
• g(x) is increasing and concave down
• g(x) is decreasing and concave up
• g(x) is decreasing and concave down

• B
• C
• D
• E

• A
• B
• C
• D

Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.

• decreasing
• increasing
• concave up
• concave down

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

• increasing
• decreasing
• concave up
• concave down

Tags

CCSS.HSF.IF.C.7

For a function f(x), f''(4)=0 indicates that x=4 is _____________.

• an inflection point
• a critical point
• a relative maximum
• a relative minimum

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down