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OLga [1]
3 years ago
9

Let f be a twice-differentiable function for all real numbers x. Which of the following additional properties guarantees that f

had a relative minimum at x=c?
(A) f’(c) = 0
(B) f’(c) = 0 and f”(c) < 0
(C) f’(c) = 0 and f”(c) > 0
(D) f’(x) > 0 for x < c and f’(x) < 0 for x > c

*the answer is not B*
Mathematics
1 answer:
Mkey [24]3 years ago
8 0

Answer:

(C) f’(c) = 0 and f”(c) > 0

Step-by-step explanation:

A minimum occurs where the first derivative is 0 (the tangent line is horizontal), and the second derivative is positive (concave up).  The simplest example of this is a positive parabola, like y = x², which has a relative minimum at its vertex.

You might be interested in
What is the equation of a line perpendicular to:
Nataly [62]

Step-by-step explanation:

"perpendicular" means it creates a right angle (90°) with the original line.

a key element is the slope (the incline) of the line.

it is the factor of x (here 1/4 for the original line) and is defined as the ratio of "y coordinate change / x coordinate change" when going from one point on the line to another.

the given slope of 1/4 means that for every increase in x by 4 units y increases by 1 unit.

now if you want to draw a few random lines, and then draw lines that cross them with a right angle, you will see very quickly the relationship of the slopes of the crossing lines :

for the slope of the perpendicular line x and y of the original slope trade places (the ratio turns "upside-down") and the sign of the slope flips (if the original line goes up, then the perpendicular line goes down and vice versa. so + turns into -, and - into +).

so, our original slope 1/4 turns into -4/1 = -4.

we still have infinite possibilities to draw such a perpendicular line (more up or more down on the coordinate grid).

to finally "nail" one particular line we need to use the given point and solve for the y-intercept.

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept (the y value for x = 0).

so, using the slope (-4) and the point (2, 5) we have

5 = -4×2 + b = -8 + b

13 = b

so, the full equation is

y = -4x + 13

7 0
2 years ago
Help me this is the last one I need to do but I'm struggling
Katarina [22]
You would multiply 2 1/2 and 3 3/4, which would give you 9.375 or as a mixed number 9 7/8
3 0
3 years ago
2-(-2x-4)=3x+6-x what is the answer to that?
ruslelena [56]

98--8=

Step-by-step explanation:

3 0
3 years ago
Can someone explain how you would write this in a equation?
Rom4ik [11]
Feet/Minute
r/t
10,000/10
Its 1000 feet every minute
Can you please answer my question from today if you can.

3 0
3 years ago
Hope made 3 different yo-yo's. She used 1 3/4 meters of string for the first yo-yo, 1 meter of string
Nat2105 [25]

Answer:

See explanation

Step-by-step explanation:

Your question is different from the attachment

Statement 1

1 adult + 5 Children

$4 for adult and total of $16 for both adult and children

Let

Cost of children skating = x

The equation is

4 + 5x = 16

Statement 2:

Cost of making a bike bag= $4

Selling price of the bike bag = $5

Profit = $16

Let x = number of bike bag

Profit = selling price - cost price

16 = 5x - 4x

16 = x(5 - 4)

Also written as

(5 - 4)x = 16

Statement 3:

Initial temperature = 16°C

Change in temperature per hour = 4°C

Final temperature = 5°C

Let

x = number of hours it changes

16 - 4x = 5

Hope made 3 different yo-yos. She used 1 3/4 meters of string for the first yo-yo, 1 meter of string for the second yo-yo, and a total of meters of string 4 1/3

length of first yo-yo = 1 3/4

length of second yo-yo = 1

Length of third yo-yo = x

Total = 4 1/3

Total length = length of first yo-yo + length of second yo-yo + length of third yo-yo

4 1/3 = 1 3/4 + 1 + x

4 1/3 = 2 3/4 + x

4 1/3 - 2 3/4 = x

13/3 - 11/4 = x

(52-33) / 12 = x

19/12 = x

x = 1 7/12

5 0
3 years ago
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