All categories

3 years ago

F(x)=x^3 −9x What is the average rate of change of over the interval [1,6]?

Mathematics

1 answer:

Inga [223]3 years ago

8 0

Answer:

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b ] = [ 1, 6 ], thus

f(b) = f(6) = 6³ - 9(6) = 216 - 54 = 162

f(a) = f(1) = 1³ - 9(1) = 1 - 9 = - 8

average rate of change = $\frac{162-(-8)}{6-1}$ = $\frac{170}{5}$ = 34

You might be interested in

Compound interest In Exercise,$3000 is invested in an account at interest rate r,compounded continuously.Find the time required

xenn [34]

Answer:

(a) 8.15

(b) 12.92

Step-by-step explanation:

Given: P = $3000, r = 0.085

$A = Pe^{rt}$

Where

A is the Amount

P is the Principal

r is the rate

t is the time

(a) For the amount to double, A = 2 × P

A = 2 × $3000

A = $6000

$6000 = 3000e^{0.085t}$

$\frac{6000}{3000} = e^{0.085t}$

$2 = e^{0.085t}$

Take $log_{e}$ of both sides

$log_{e}2 = log_{e}e^{0.085t}$

But $log_{e}e = 1$

∴ $ln2 = 0.085t$

$t = \frac{ln2}{0.085}$

$t = \frac{0.693}{0.085}$

t = 8.15

(b) For the amount to double, A = 3 × P

A = 3 × $3000

A = $9000

$9000 = 3000e^{0.085t}$

$\frac{9000}{3000} = e^{0.085t}$

$3 = e^{0.085t}$

Take $log_{e}$ of both sides

$log_{e}3 = log_{e}e^{0.085t}$

But $log_{e}e = 1$

∴ $ln3 = 0.085t$

$t = \frac{ln3}{0.085}$

$t = \frac{1.0986}{0.085}$

t = 12.92

5 0

3 years ago

Is this set closed or not closed under the operation ? Negative integers under multiplication

Romashka [77]

The set is not closed

Example:

-4 * -3 = 12 this is not a negative integer

5 0

3 years ago

Help me on this problem please!

nexus9112 [7]

The answer is 'F'.......

4 0

3 years ago

Read 2 more answers

A shipment of 105 Otter box covers for I-phones has arrived. The total invoice (excluding tax, shipping, etc.) is $3,849.75.

bezimeni [28]

<span>3,849.75 </span>÷ 49.95 = 77 (Calculator)

Sense you would like it explained than the question is asking how many otter box Defender Covers where shipped in that price. So when you have that they want the amount of Otter Box Defenders than you divide the amount paid for the shipment with the amount of the otter box defender price.

I hope this is helpful.

3 0

4 years ago

The current population of a small town is 10,500, and its population is expected to grow at a rate of 5% per year. Which of the

FromTheMoon [43]

Answer:

f(x) = 10,500 x 1.05^t

8 0

3 years ago