End of course review--application of differentiation

Local maximum point is obtained when

• f ' (x) exchange from negative to positive

• f '' (x) exchange from positive to negative

• f ' (x) exchange from positive to negative

• f '' (x) exchange from negative to positive

Local minimum point is obtained when

• f ' (x) exchange from negative to positive

• f '' (x) exchange from positive to negative

• f ' (x) exchange from positive to negative

• f '' (x) exchange from negative to positive

Over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)
• (-3, 1)
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSS.ID.C.7

 If (a,b) is a local minimum, then what will be true about f'(a)?

• It's positive
• It's negative
• It's zero
• Cannot be determined

Concave upward is obtained when

• f '' is negative

• f ' is positive

• f ' is negative

• f '' is positive

Tags

CCSS.HSF-IF.C.7A

Concave downward is obtained when

• f '' is negative

• f ' is positive

• f ' is negative

• f '' is positive

Tags

CCSS.HSF-IF.C.7A

A spherical ball is being inflated at a rate of 20 $\frac{cm^3}{s}$  . Find the rate of increase of its radius when it's surface area is  $100\pi\ cm^2$  

•  $\frac{1}{6\pi}$   cm/s

•  $\frac{1}{4\pi}$   cm/s

•  $\frac{1}{5\pi}$  cm/s

•  $\frac{2}{5\pi}$   cm/s

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

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