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Dahasolnce [82]

4 years ago

10

The following are the weights, in pounds, of some dogs at a kennel: 36, 45, 29, 39, 51, 49

1 answer:

MAXImum [283]4 years ago

5 0

What is the question...??

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Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)= 6x^1/3 + 3x^4/3. You must justify

irina [24]

Answer:

x-coordinates of relative extrema = $\frac{-1}{2}$

x-coordinates of the inflexion points are 0, 1

Step-by-step explanation:

$f(x)=6x^{\frac{1}{3}}+3x^{\frac{4}{3}}$

Differentiate with respect to x

$f'(x)=6\left ( \frac{1}{3} \right )x^{\frac{-2}{3}}+3\left ( \frac{4}{3} \right )x^{\frac{1}{3}}=\frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}$

$f'(x)=0\Rightarrow \frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}=0\Rightarrow x=\frac{-1}{2}$

Differentiate f'(x) with respect to x

$f''(x)=2\left ( \frac{-2}{3} \right )x^{\frac{-5}{3}}+\frac{4}{3}x^{\frac{-2}{3}}=\frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}\\f''(x)=0\Rightarrow \frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}=0\Rightarrow x=1$

At x = $\frac{-1}{2}$ ,

$f''\left ( \frac{-1}{2} \right )=\frac{4\left ( -1+4\left ( \frac{-1}{2} \right ) \right )}{3\left ( \frac{-1}{2} \right )^{\frac{5}{3}}}>0$

We know that if $f''(a)>0$ then x = a is a point of minima.

So, $x=\frac{-1}{2}$ is a point of minima.

For inflexion points:

Inflexion points are the points at which f''(x) = 0 or f''(x) is not defined.

So, x-coordinates of the inflexion points are 0, 1

7 0

3 years ago

Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 30 more adult tickets than student tick

Arada [10]

8a+4s=840
a=s+30
8(s+30)+4s=840
12s+240=840
12s=600
s=50

A=s+30
a=50+30
a=80

The drama play sold 80 adult tickets

8 0

3 years ago

The sum of three consecutive numbers is 87. What is the smallest of the three numbers?

Jobisdone [24]

Answer:

10

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Please help solve for Z

Brilliant_brown [7]

The second one Z=-11

3 0

3 years ago

11 halves divided by 7

Tamiku [17]

Answer:

$\large\boxed{\dfrac{11}{14}}$

Step-by-step explanation:

$\dfrac{\frac{11}{2}}{7}=\dfrac{11}{2}\div7=\dfrac{11}{2}\div\dfrac{7}{1}=\dfrac{11}{2}\cdot\dfrac{1}{7}=\dfrac{(11)(1)}{(2)(7)}=\dfrac{11}{14}$

4 0

4 years ago

Read 2 more answers