Answer:
x-coordinates of relative extrema = ![\frac{-1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B2%7D)
x-coordinates of the inflexion points are 0, 1
Step-by-step explanation:
![f(x)=6x^{\frac{1}{3}}+3x^{\frac{4}{3}}](https://tex.z-dn.net/?f=f%28x%29%3D6x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%2B3x%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D)
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}}](https://tex.z-dn.net/?f=f%27%28x%29%3D6%5Cleft%20%28%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29x%5E%7B%5Cfrac%7B-2%7D%7B3%7D%7D%2B3%5Cleft%20%28%20%5Cfrac%7B4%7D%7B3%7D%20%5Cright%20%29x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%5Cfrac%7B2%7D%7Bx%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%2B4x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![f'(x)=0\Rightarrow \frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}=0\Rightarrow x=\frac{-1}{2}](https://tex.z-dn.net/?f=f%27%28x%29%3D0%5CRightarrow%20%5Cfrac%7B2%7D%7Bx%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%2B4x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D0%5CRightarrow%20x%3D%5Cfrac%7B-1%7D%7B2%7D)
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](https://tex.z-dn.net/?f=f%27%27%28x%29%3D2%5Cleft%20%28%20%5Cfrac%7B-2%7D%7B3%7D%20%5Cright%20%29x%5E%7B%5Cfrac%7B-5%7D%7B3%7D%7D%2B%5Cfrac%7B4%7D%7B3%7Dx%5E%7B%5Cfrac%7B-2%7D%7B3%7D%7D%3D%5Cfrac%7B-4x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%2B4x%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%7D%7B3x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7Dx%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%7D%5C%5Cf%27%27%28x%29%3D0%5CRightarrow%20%5Cfrac%7B-4x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%2B4x%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%7D%7B3x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7Dx%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%7D%3D0%5CRightarrow%20x%3D1)
At x =
,
![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](https://tex.z-dn.net/?f=f%27%27%5Cleft%20%28%20%5Cfrac%7B-1%7D%7B2%7D%20%5Cright%20%29%3D%5Cfrac%7B4%5Cleft%20%28%20-1%2B4%5Cleft%20%28%20%5Cfrac%7B-1%7D%7B2%7D%20%5Cright%20%29%20%5Cright%20%29%7D%7B3%5Cleft%20%28%20%5Cfrac%7B-1%7D%7B2%7D%20%5Cright%20%29%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%7D%3E0)
We know that if
then x = a is a point of minima.
So,
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
The answer to N is 5
Step-by-step explanation:
Multiply 7 × 5=35, Then you subtract it by 4, then you get 31.
The increase in price is 140% of the original price.
The original price was 100% of the original price since 100% is a whole quantity.
Now the new price is 140% more than it was, so the new price is
100% + 140% of the old price.
100% + 140% = 240%
Now we find 240% of $50.
To find a percent of a number, multiply the percent by the number.
240% of $50 =
= 240% * $50
= 2.4 * $50
= $120
Answer: 10 ft of gold wire now costs $120
Gold wire now costs $12 per foot.
Answer:
4
Step-by-step explanation:
2x + 3x + 4x = 36
Evaluate like terms.
9x = 36
Find x.
x = 36 ÷ 9
x = 4