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3 years ago

Rewrite the equation below so that it does not have fractions.

Mathematics

1 answer:

Vlad1618 [11]3 years ago

8 0

Answer:

9x=38

Step-by-step explanation:

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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

bob has 20 apples, billy has 20 pears, bob gives 4 pears to his little sister, billys uncle gives him 69 bananas. What is the di

AysviL [449]

Answer:

Step-by-step explanation:

Bob

20-4=16

Billy 20+69=89

89-16=73

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2 years ago

Does cheese smell good?

aivan3 [116]

Answer:

Step-by-step explanation:

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3 years ago

A quality control technician checked a sample of 30 bulbs. Two of the bulbs were defective. If the sample was a representative,

bogdanovich [222]

I think that 30 bulbs are expected to be defective.

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3 years ago

Suppose the line of best fit for some data points has a slope of 4.915. If the mean of the x-coordinates of the data points is 1

8_murik_8 [283]

Using the slope-intercept formula, y=mx+b where m is the slope of the line and b being the y-intercept, by direct substitution, the y-intercept can be directly be obtained,
y=mx+b
14.347 = (4.915)(10.088) + b
therefore, the y-intercept, b = -35.236

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3 years ago

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