Calculus Review - Applications of Derivatives

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle? 

• v(t) = -2
• v(t) -2t - 1 
• v(t) = t³
• v(t) = -t

Where does the function, f(x) = 2x³ - 9x² + 12x -3 have relative max/min values?

• Rel max x = -1, Rel min x = 2

• Rel min x = 1, Rel min x = 2

• Rel max x = 1, Rel min x = 2

• Rel max x = 2, Rel min x = 1

Let f be the function with derivative given by f'(x) = x² - 2/x. On which of the following intervals is f decreasing?

• (-∞, 0]

• (-1, 0]

• (0, ∛2]

• (∛2, ∞)

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

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

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

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0
• -1
• 2
• 5

Tags

CCSS.HSA.APR.B.3

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

What is a point of inflection?

• When a function goes from increasing to decreasing
• When a function goes from concave up to concave down

If a function has a second derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down