Analysis of Functions

Identify the interval from the derivative graph where the function is concave up.

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

Identify the interval from the derivative graph where the function is concave down

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

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

Use the sign chart for f'(x).  There is(are) ...

• a local maximum at x = -2.
• a local minimum at
  x = -2 and a local maximum at x = 4.
• a local maximum at
  x = -2 and a local minimum at x = 4.
• no extrema.

If given a graph of f'(x) how do you determine the values of x at which f (x) has a relative maximum?

• f'(x) has a change in values from positive to negative
• f'(x) has a change in values of y from negative to positive
• Value of f'(x) = 0
• Value of f'(x) DNE

f' is given, which could be f?

• A
• B
• C

List all of the x-locations of the minimum points of the function whose derivative is graphed.

• {-2, 1}
• {-1, 1}
• {-1}
• Cannot be determined}

List all of the x-locations of the points of inflection of the function whose derivative is graphed.

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

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

Tags

CCSS.HSF.IF.B.4

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