Fundamental Theorem of Calculus (f, f', and f'')

_{Evaluate the integral}

• 30/3
• 31/3
• 29/3
• 32/3

Tags

CCSS.HSA.APR.A.1

• 1 ⁄ (1+x³) 
• (3x²) ⁄ (1+x³) 
• x³  ⁄ (1+x³) 
• HELP

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Evaluate in terms of area
 $\int_0^2f\left(x\right)dx$  

• 4

• -4

• 4 + 2π

• -4 - 2π

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

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

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

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

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

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

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

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7