First Derivative Test

Where is

 $f\left(x\right)=5x^3-5x^2$  increasing?

•  $\left(-\infty,0\right)$  

•  $\left(-\infty,0\right)U\left(\frac{2}{3},\infty\right)$  

•  $\left(\frac{2}{3},\infty\right)$  

•  $\left(0,\frac{2}{3}\right)$  

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

Tags

CCSS.HSF.IF.B.4

when you check for sign changes at the critical points of a function, you are using the

• IVT

• MVT

• 1st Derivative Test

• 2nd Derivative Test

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.

Tags

CCSS.HSA.APR.B.3

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)

• (-∞, -√3) ∪ (0, √3)

• (-1, 1)

• (-√3, 0) ∪ (√3, ∞)

Tags

CCSS.HSA.REI.D.10

True or false: all critical points are extrema

• True

• False

Tags

CCSS.HSF.IF.C.7

CCSS.HSA.REI.D.10

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0
• -1
• 2
• 5

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the open interval(s) where the function is increasing:

 $f\left(x\right)=-x^3-10x^2-32x-32$  

•  $\left(-\infty,-\frac{4}{3}\right),\left(-\frac{8}{9},\infty\right)$  

•  $\left(-4,-\frac{8}{3}\right)$  

•  $\left(-\infty,-4\right),\left(-\frac{8}{3},\infty\right)$  

•  $\left(-16,-\frac{32}{3}\right)$  

Tags

CCSS.HSA.APR.B.3

Find the open interval(s) where the function is decreasing.

 $y=-\frac{x^2}{2x+2}$  

•  $\left(-2,-1\right),\left(-1,0\right)$  

•  $\left(-\infty,-8\right),\left(4,\infty\right)$  

•  $\left(-\infty,-2\right),\left(0,\infty\right)$  

•  $\left(-\frac{2}{3},-\frac{1}{3}\right),\left(-\frac{1}{3},\frac{1}{3}\right)$  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

For the function given, identify the point(s) of relative minima.

 $y=\cos\left(x\right)\ ;\ \left[0,2\pi\right]$  

•  $x=\pi$  

•  $x=0$  

•  $x=\left\{-\frac{\pi}{4},\frac{3\pi}{4},-\pi,\pi\right\}$  

• No points of relative minima