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3 years ago

7

Let f be a function such that f(2) ≤ f(x) for all values of x in the interval (0, 3). Does f(2) represent a relative minimum or

a relative maximum?

1 answer:

Dmitry_Shevchenko [17]3 years ago

7 0

Answer: f(2) is a relative minimum

This is because f(2) is the lowest y output for any given y = f(x) output on the interval $0 < x < 3$ which is what the interval notation (0,3) indicates.

Draw out a "parabolic" like shape where the lowest point occurs at (2, f(2)), where f(2) is unknown, but we at least know that x = 2. I put "parabolic" in quotes because it may not be a true parabola, but it looks like one. This lowest point only applies for the neighbor hood $0 < x < 3$ .

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Use matrix addition to solve this equation: B + 15 −7 4 0 1 2 = 1 2 12 4 0 2 b11 = b12 = b13 = b21 = 4 b22 = −1 b23 = 0

Arada [10]

Answer:

$b_{11}=-14,b_{12}=9,b_{13}=8,b_{21}=4,b_{22}=-1,b_{23}=0$

Step-by-step explanation:

The given matrix addition is

$B+\begin{bmatrix}15&-7&4\\ 0&1&2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}$

We need to find the elements of matrix B.

Let $B=\begin{bmatrix}b_{11}&b_{12}&b_{13}\\ b_{21}&b_{22}&b_{23}\end{bmatrix}$

Substitute the value of matrix.

$\begin{bmatrix}b_{11}&b_{12}&b_{13}\\ b_{21}&b_{22}&b_{23}\end{bmatrix}+\begin{bmatrix}15&-7&4\\ 0&1&2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}$

After addition of two matrix we get

$\begin{bmatrix}b_{11}+15&b_{12}-7&b_{13}+4\\ b_{21}+0&b_{22}+1&b_{23}+2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}$

On equating both sides.

$b_{11}+15=1\Rightarrow b_{11}=-14$

$b_{12}-7=2\Rightarrow b_{12}=9$

$b_{13}+4=12\Rightarrow b_{13}=8$

$b_{21}+0=4\Rightarrow b_{21}=4$

$b_{22}+1=0\Rightarrow b_{22}=-1$

$b_{23}+2=2\Rightarrow b_{23}=0$

Therefore, the elements of matrix B are $b_{11}=-14,b_{12}=9,b_{13}=8,b_{21}=4,b_{22}=-1,b_{23}=0$ .

3 0

3 years ago

This is the graph of f(x). What is the value of f(3)?

Paul [167]

Answer:

The value of f(3) is 8 ⇒ D

Step-by-step explanation:

In the function f(x) = y, y is the corresponding value of x

Ex: If f(a) = b, then the value of y = b at x = a

Let us solve the question

∵ The given figure represents the function f(x)

→ That means every point on the graph represents f(x) = y

∴ f(x) = y

∵ We need to find f(3)

→ That means we need the value of y at x = 3

∴ x = 3

Look at the graph and find the y-coordinate of the point that lies on the curve and has x-coordinate = 3

→ Each small square on the x-axis represents 1 unit, and on the y-axis

represents 2 units

∵ There is a point on the graph that has x-coordinate = 3

∵ The y-coordinate of this point is 8

∴ The point (3, 8) lies on the graph of f(x)

∴ x = 3 and y = 8

∴ f(3) = 8

∴ The value of f(3) is 8

7 0

2 years ago

Sketch the graph of y =sine3x

IgorLugansk [536]

The graph of $\mathbf{y=\sin{3x}}$ is given by,

Here given the function is $y=\sin{3x}$

when $x=0\Rightarrow y=\sin{3\times 0}=\sin0=0$ , then it passes through the origin (0,0).

When $x=\frac{\pi}{6}\Rightarrow y=\sin{3\times\frac{\pi}{6}}=\sin\frac{\pi}{2}=1$

Since we know that, $-1\leq\sin{x}\leq1,\forall x$ , then the function has maximum height at $x=\frac{\pi}{6}$ .

Again when $x=\frac{\pi}{3}\Rightarrow y=\sin{(3\times\frac{\pi}{3})}=\sin\pi=0$ , again the function is 0.

So clearly the function is the Oscillating function.

Using graphing calculator we get the graph of function $y=\sin3x$ ,

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8 0

1 year ago

Mrs Perry shares out 21 biscuits between

avanturin [10]

Answer:

Gemma gets 3 biscuits

Zak gets 18 biscuits

Step-by-step explanation:

1:6 = 1+6

= 7

1/7 * 21 = 3

6/7 * 21 = 18

4 0

3 years ago

Read 2 more answers

Convert 5 whole number and 7 over 8 into an improper fraction

Len [333]

Answer: 47/8

Step-by-step explanation: To write a mixed number as an improper fraction, first multiply the denominator by the whole number and then add the numerator. Finally, we will put our new number over our old denominator and we have our answer which is 47/8.

Therefore, $5\frac{7}{8}$ can be rewritten as the improper fraction 47/8.

7 0

2 years ago