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Effectus [21]
3 years ago
6

The following data points represent the number of toppings each customer at I Scream Sundae Shop put on their ice cream.

Mathematics
2 answers:
dolphi86 [110]3 years ago
6 0

Answer:

5.5

Step-by-step explanation:

lakkis [162]3 years ago
3 0

Answer:

Step-by-step explanation:

34

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Find the critical numbers of the function f(x) = x6(x − 1)5 what does the first derivative test tell you that the second derivat
patriot [66]
The given function is f(x) = x⁶(x-1)⁵

The first derivative is
f'(x) = 6x⁵(x-1)⁵ + 5x⁶(x-1)⁴
       = x⁵(x-1)⁴(6x - 6 + 5x)
       = x⁵(x-1)⁴(11x - 6)
The critical values are the zeros of f'(x). They are
x = 0, 6/11, and 1.
The critical values indicate that turning points exist for f(x) at the critical points. However, we do not know the nature of the turning points.

Write the first derivative in the form f'(x) = (x-1)⁴(11x⁶ - 6x⁵).
The second derivative is
f''(x) = 4(x-1)³(11x⁶ - 6x⁵) + (x-1)⁴(66x⁵ - 30x⁴)
        = (x-1)³(44x⁶ - 24x⁵ + 66x⁶ - 30x⁵ - 66x⁵ + 30x⁴)
        = (x-1)³(110x⁶ - 120x⁵ + 30x⁴)
        = 10x⁴(x-1)³(11x² - 12x + 3)
The sign of f''(x) at the critical values tell us the nature of the turning point.

f''(0) = 0, therefore a point of inflection exists at x = 0.
f''(6/11) > 0, therefore a local minumum exists at x = 6/11.
f''(1) = 0, therefore a point of inflection exists at x=1.

The graphs shown below confirm these results.

8 0
3 years ago
Solve the following equation for x, in terms of a and b <br><br> ax= 15+bx
ZanzabumX [31]
Ax=15+bx
ax-bx=15
x(a-b)=15
x=15/(a-b)

4 0
3 years ago
What is the sum -1 1/5 + (-3/5)
son4ous [18]

Answer:

-14/5

Step-by-step explanation:

-11 - 3= -14 and the denominator stays the same.

3 0
3 years ago
What is 5- (t+3)= -1+2(t-3)
maks197457 [2]

Answer:

Step-by-step explanation:

t=3

7 0
2 years ago
Read 2 more answers
There are four brands of smart phones that are most popular in United States. The number of people in United States that have ea
GREYUIT [131]
So what is the question?

5 0
4 years ago
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