FA- AP Derivative and Integral Review (R)

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

• The function is increasing
• The function is decreasing

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

• The function is increasing
• The function is decreasing

Tags

CCSS.HSF.IF.B.4

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

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

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

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

Where is the point of inflection for the function  $f\left(x\right)\ =\ x^{3\ }+6x^2$  ?

•  $x=0$  

•  $x=-4$  

•  $x=-2$  

•  $x=4$  

A function is increasing if its first derivative is what?

• undefined

• positive

• negative

• zero

Critical numbers occur where the first derivative is what? (Check all that apply).

• endpoint

• zero

• maximum

• undefined

The derivative of a function is its

• Slope
• Maximum/Minimum
• Instantaneous rate of change
• Common Denominator

Find the derivative of  f(x) = (x⁶ + 4)⁵

• f '(x) = 5x⁵(x⁴ + 4)⁴
• f '(x) = 6x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁶(x⁶ + 4)⁴