All categories

2 years ago

7. If F(x) = f(g(x)), where f(-2) = 8, f'(-2) = 4, f'(5) = 3, g(5)=-2, gʻ(5) = 6.. Find F'(5)

Mathematics

2 answers:

serious [3.7K]2 years ago

7 0

Answer:

I'm going to lay this out in a chart so it's a little easier to see:

F(x) = f(g(x))

x | f (x) | f ' (x) | g (x) | g ' (x)

--------------------------------------

-2 | 8 | 4 |

5 | | 3 | -2 | 6

Remember the chain rule, which says

(f (g (x))) ' = g ' (x) f ' (g (x))

When they ask for F ' (5), they are asking for (f (g (x))) ' when x = 5.

Using the chain rule, that's

F ' (5) = g ' (5) f ' (g (5))

We can simplify using the numbers provided.

F ' (5) = (6) f ' (-2)

F ' (5) = (6) (4)

F ' (5) = 24

I hope that helps!

by jannat <33

Dovator [93]2 years ago

4 0

Step-by-step explanation:

I'm going to lay this out in a chart so it's a little easier to see:

F(x) = f(g(x))

x | f (x) | f ' (x) | g (x) | g ' (x)

--------------------------------------

-2 | 8 | 4 |

5 | | 3 | -2 | 6

Remember the chain rule, which says

(f (g (x))) ' = g ' (x) f ' (g (x))

When they ask for F ' (5), they are asking for (f (g (x))) ' when x = 5.

Using the chain rule, that's

F ' (5) = g ' (5) f ' (g (5))

We can simplify using the numbers provided.

F ' (5) = (6) f ' (-2)

F ' (5) = (6) (4)

F ' (5) = 24

I hope that helps!

You might be interested in

in a sale normal prices are reduced by 15%. the sale price of a CD player is $102. work out the normal price of the CD player.

morpeh [17]

.85x=102
x=120
The answer is $120.

8 0

2 years ago

Which of the following could lead to a misleading graph?

natima [27]

Answer:

The intervals on the y-axis are inconsistent.

Step-by-step explanation:

The x- and y-axes start at 0 - this is what graphs normally start with - it is out of the norm to not start at 0.

The intervals on the y-axis are inconsistent - this can cause a problem - we humans tend to judge a graph on height, so changing some of the intervals can mess up a human's actions based on the graph,for example people might think more positively or negatively of a brand or company, and even a totally different view.

The intervals on the y and x-axis are different - they can be different for particular reasons, for example a company might want to put time intervals in months on the x-axis and revenue in dollars on the y-axis - sometimes it is just necessary.

Differing heights are used on a bar graph - this allows us to compare data - without it we would not be able to do much with it.

3 0

2 years ago

Rewrite using a single positive exponent. 6^5 6

Fiesta28 [93]

Answer:

$6^{4}$