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3 years ago

Find the value of the given function's derivative at x=3

Mathematics

1 answer:

Rasek [7]3 years ago

7 0

<h2>Explanation:</h2>

According to the chain rule, if we have a function:

$f(x)=k(g(x))$

The derivative at a point $a$ will be:

$f'(a)=k'(g(a))g'(a)$

We know that:

$f'(3)=k'(g(3))g'(3)\\ \\ \\ a=3 \\ \\ \\ Then: \\ \\ g(3)=2(3)-3^2 \\ \\ g(3)=6-9 \\ \\ g(3)=-3 \\ \\ \\ k'(g(3))=k'(-3)=2 \\ \\ \\ g'(x)=2-2x \\ \\ g'(3)=2-2(3)=-4 \\ \\ \\ Finally: \\ \\ f'(3)=2(-4) \\ \\ \boxed{f'(3)=-8}$

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Answer:

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Step-by-step explanation:

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2 years ago

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Hera spent $16 on dinner then she spent $6 on dessert and some more on a taxi ride including the taxi fair she spent a total of

s344n2d4d5 [400]

She spent $9.

$16+$6 is $22, so the total $31 minus $22 leaves us with the $9 she spent for the taxi.

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3 years ago

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PLEASE HELP!<br><br> Question is on photo! <br> Thank you!!

ipn [44]

We conclude that the relation presented in the picture is a function with domain: - 4 ≤ x < 1 and range: - 4 ≤ x ≤ 5. (Correct choices: B, C, H)

<h3>How to determine the domain and range of a relation and if a relation is a function</h3>

Herein we have a relation between two variables, x and y, relations involve two sets: an input set called domain and an output set called range. A relation is a function if and only if every element of the domain is related to only one element from the range.

Graphically speaking, the horizontal axis corresponds with the domain, whereas the vertical axis is for the set of the range. According to the previous concepts, we conclude that the relation presented in the picture is a function with domain: - 4 ≤ x < 1 and range: - 4 ≤ x ≤ 5. (Correct choices: B, C, H)

To learn more on functions: brainly.com/question/12431044

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1 year ago

Find the area of the shaded regions below. Give your answer as a completely

Eddi Din [679]

Answer:

$\huge\boxed{A_R=18\pi\ cm^2}$

Step-by-step explanation:

$\dfrac{80^o}{360^o}=\dfrac{8}{36}=\dfrac{2}{9}$

The shaded region is 2/9 of whole circle.

Calculate the area of a circle:

$A=\pi r^2$

$r$ - radius

Substitute $r=9cm$

$A_O=\pi\cdot9^2=81\pi(cm^2)$

Calculate the area of the shaded regions:

$A_R=\dfrac{2}{9}A_O\\\\A_R=\dfrac{2}{9}\cdot81\pi=2\cdot9\pi=18\pi(cm^2)$

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2 years ago

Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system.

FrozenT [24]

Given:

The system of inequalities:

$x>3$

$y$

To find:

The point that represents a solution to the system by using the graph.

Solution:

We have,

$x>3$

$y$

The related equations of these inequalities are:

$x=3$

$y=2x-5$

The line $x=3$ is a vertical line that intersect the x-axis at 3.

The table of values for $y=2x-5$ is:

x y

0 -5

1 -3

Plot (0,-5) and (1,-3) on a coordinate plan and connect them by a straight line.

The boundary lines are dotted lines because the points on the lines are not included in the solution set.

Check the inequalities for (0,0).

First inequality: $0>3$ ( False)

Second inequality: $0$

$0$ (False)

Both inequalities are false for (0,0). It means the shaded region of the lines is in the opposite direction of (0,0).

Plot the shaded region and the points (-3, -1), (1, 11), (4, -1), (5, 6) as shown in the below graph.

From the below graph, it is clear that the point (4,-1) is the only point lies in the common shaded region. So, (4,-1) represents a solution to the system.

Therefore, the correct option is C.

5 0

3 years ago