Derivative tests

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

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSF.LE.B.5

If the 1st derivative is positive on a certain interval, then that interval is decreasing.

• True (Facts)

• False (Not Facts)

If the first derivative of a function changes from positive to negative at a certain point, then that point is a known as a relative minimum.

• True (Facts)

• False (Not Facts)

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

• increasing
• decreasing
• concave up
• concave down

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

• increasing
• decreasing
• concave up
• concave down

The graph shown is the DERIVATIVE of f. From the derivative's graph, identify the interval graph where f (the original function) is concave up.

• (-1,1) & (3,4)
• (-3,-2)
• (-2,-1)
• (-3,-1) & (1,3)

If f''(x)>0 over the interval (-7,1), then what will be true about f'(x)?

• It's constant
• It's increasing
• It's decreasing
• Cannot be determined

Tags

CCSS.HSF.IF.B.4

List all of the critical values (x-locations of the critical points) of the function whose derivative is graphed.

• {-3, -1, 1}
• {-3, -1}
• {-4, -2, 0}
• Cannot be determined