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4 years ago

Find the maximum value of the function

Mathematics

2 answers:

timama [110]4 years ago

8 0

$\bf \stackrel{f(x)}{y}=1-x-x^2\implies y=-x^2-x+1
\\\\\\
\textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{lccclll}
y = &{{ -1}}x^2&{{ -1}}x&{{ +1}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)
\\\\\\
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad \stackrel{maximum}{1-\cfrac{(-1)^2}{4(-1)}}\right)$

romanna [79]4 years ago

6 0

The maximum value of the function is 5/4.

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3 years ago

How can you find a function that has these roots?

EleoNora [17]

Answer:

The quadratic function x^2 - 5x + 6 =0

can be factored into (x -3) * (x-2)

And it would have roots of 3 and 2

So, if a cubic functions has roots of 2, 3 and 5 then its factors are

(x -2)* (x -3) * (x -5)

Multiply it out to get the equation.

Dunno if that was what you were looking for but i did what i can....

7 0

3 years ago

A marshy region used for agricultural drainage has become contaminated with a particular element. It has been determined that fl

kipiarov [429]

Answer:

8.49%

Step-by-step explanation:

x months

$f(x) =\frac{x^2+64}{2x}$ 1 ≤ x ≤ 12

minimum: $f'(x) = 0$

$f'(x) = (\frac{x^{2} +64}{2x})' = \frac{(x^{2} +64)'.2x - (x^{2} +64).(2x)'}{(2x)^2}= \frac{2x.2x-(x^{2}+64).2}{4x^{2} } = \frac{4x^2 - 2x^2-64}{4x^2}=\frac{2x^2-64}{4x^2}$

$\frac{x^2-32}{2x^2} = 0 \\x^{2} -32 = 0\\x^{2} =32\\x = \sqrt{32}\\ x = 4\sqrt{2}$

$f(4\sqrt{2} ) = \frac{(4\sqrt{2})^2 +64}{2.4\sqrt{2} } = \frac{32+64}{8\sqrt{2} } = \frac{96}{8\sqrt{2} }=\frac{12}{\sqrt{2} } = 6\sqrt{2}$ ≅8.49%

5 0

3 years ago

Komok [63]

<h2>54 units²</h2><h2 />

This is a compound shape. You can split it into x shapes. See Attachment

Rectangle - Red

Area of a Rectangle = L × B

L = 7

B = 6

7 × 6 = 42

<h3>42 units²</h3>

Triangle - Orange

Area of a Triangle = 1/2BH

B = 6

H = 1

1/2 × 6 × 1 = 3

<h3>3 units²</h3>

Triangle - Green

Area of a Triangle = 1/2BH

B = 3

H = 2

1/2 × 3 × 2 = 3

<h3>3 units²</h3>

Triangle - Blue

Area of a Triangle = 1/2BH

B = 2

H = 6

1/2 × 2 × 6 = 6

<h3>6 units²</h3><h3 /><h3>42 + 6 + 3 + 3 = 54</h3>

7 0

3 years ago

Read 2 more answers

Please help guys I will be helping u in following days for sure

Firlakuza [10]

Answer:

Step-by-step explanation:

Hope this helps u !!

5 0

3 years ago