5.3 Connecting f` and f`` with the graph of the function

5.3 Connecting f^, and f^{,,
with the graph of f}

Multiple Select

f(x)=x³-12x-5

• Relative max. 0 at x=-1

• Relative max. 11 at x=-2

• Relative min. -21 at x=2

• Relative min. 9 at x=8

Multiple Select

f(x)=x²-x-1

• Relative max. 0 at x=-1

• Relative max. 11 at x=-2

• Relative min. -5/4 at x=1/2

  and

  Abs. Min

• Abs. max. 3 at x=9

Multiple Select

f(x)=-2x³ +6x² -3

• Relative min. -3 at x=0

• Relative max. 5 at x=2

• Relative min. -5/4 at x=1/2

  and

  Abs. Min

• Abs. max. 3 at x=9

Multiple Choice

f(x) is increasing when

Multiple Choice

f(x) is decreasing when

Multiple Choice

f(x) has a relative max. hen

• f^`(x) change signs from - to +

• f^`(x) change signs from + to -

Multiple Choice

f(x) has a relative min. when

• f^`(x) change signs from - to +

• f^`(x) change signs from + to -

Multiple Choice

The first derivative test is used to determine

• Relative max. and Min.

• Absolute max. and min.

• concave up

• concave dawn

Multiple Choice

for a function g(x) , g^`(5)=0 indicates that x=5 is

• abs. min

• critical point

• inflection point

• abs. max.

Multiple Choice

When f^{`</sup>(x)=0 or f<sup>`}(x) is undefined you get..

• area under the curve

• inflection point

• extreme

• critical point

Multiple Select

When f^`(x)=0 you get..

• Stationary point

• inflection point

• extreme

• critical point

​​Concavity

​​Concavity

Multiple Select

f(x) is concave down when

• f`(x) decreasing

  f`(x)<0

• f`(x) Increasing

  f`(x)>0

Multiple Select

f(x) is concave up when

• f`(x) decreasing

  f`(x)<0

• f`(x) Increasing

  f`(x)>0

Multiple Select

The second derivative test is used to determine

• Relative max. and Min.

• Absolute max. and min.

• interval of concave up

• interval of concave dawn

Multiple Choice

f(x)=x² on (3,10)

• Relative max.

• Abs. max.

• Relative min.

• Concave up.

​​Point of Inflection

​​f``(x)=0

Multiple Select

f(x)=4x³ +21x² +36x-20

• Concave dawn

  (- $$\infty$$ ,-7/4)

• Concave up. (0,2)

• Concave up.

  (-7/4, $$\infty$$ )

Multiple Select

f(x)=-x⁴ +4x³ -4x+1

• Concave dawn (- $$\infty$$ ,0) and (2, $$\infty$$ )

• Concave dawn

  (- $$\infty$$ ,-7/4)

• Concave up. (0,2)

Multiple Select

use the graph of the function f' to estimate the intervals on which the function fis (a) increasing or (b) decreas- ing. Also, (c) estimate the x-coordinates of all local extreme values.

• Increase (- $$\infty$$ ,-2) and (0,2)

• Decrease (-2,0)and (2, $$\infty$$ )

• Relative(local) max.

  at x=-2,2

• Relative(local)min. at x=0

Multiple Select

use the graph of the function f' to estimate the intervals on which the function fis (a) increasing or (b) decreas- ing. Also, (c) estimate the x-coordinates of all local extreme values.

• Increase

  (-2,2)

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

  and (2, $$\infty$$ )

• Relative(local) max.

  at x=2

• Relative(local)min. at x=-2

​​Second Derivative test for Local(Relative)Extreme

Multiple Select

f(x)=x³ -12x-5

• Relative(local) max.

  at x=-2

• Relative(local)min. at x=2

• Relative(local) max.

  at x=2

• Relative(local)min. at x=-2