All categories

3 years ago

Find maximum points y=11^(6x-x²) solve using derivative

Mathematics

1 answer:

Darya [45]3 years ago

8 0

Answer:

$\boxed{\sf \ \ \ maximum \ is \ 11^9=2357947691 \ \ \ }$

Step-by-step explanation:

hello

$y = 11^{(6x-x^2)}=exp((6x-x^2)ln(11))$

so to know the maximum to y we can check the maximum of

f(x)= $6x-x^2$

f is derivable and f'(x)=6-2x

f'(x)=0 <=> x = 3

so the maximum is reached for x = 3

f(3)=18-9=9

and then

$y = 11^9=2357947691$

to be rigorous, we can write the variation table of y to show that there is only one maximum

hope this helps

You might be interested in

Evaluate f(x) = 4x + 3x^2 − 5 when x = -2. 23 -1 -25 -49

frozen [14]

Answer:

f(-2) = -1

Step-by-step explanation:

One way of doing this is to substitute -2 for x in every place where x shows up:

f(x) = 4x + 3x^2 − 5 → f(-2) = 4(-2) + 3(-2)^2 − 5

→ f(-2) = -8 + 3(4) - 5, or f(-2) = 4 - 5, or f(-2) = -1

5 0

3 years ago

Country A has a growth rate of 4.9% per year. The population is currently 4 comma 151,000, and the land area of Country A is 1

kvv77 [185]

Answer:

There will be one person on 1 square yard of land after 1,892,147.588 years.

Step-by-step explanation:

Continuous exponential growth formula:

$P(t)=Pe^{rt}$

P(t)= Population after t years.

P= Initial population

r=rate of growth.

t= time in year

Given that,

Growth rate of country A (r)= 4.9% per year=0.049 per year.

Initial population (P)= 151,000.

Land area of country area= 14,000,000,000 square yards.

There will be one person on one square yard of land.

So, there will be 14,000,000,000 person for 14,000,000,000 square yard of land in country A.

P(t)=14,000,000,000 person

$\therefore 14,000,000,000= 151,000 e^{0.049t}$

$\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}$

Taking ln both sides

$\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|$

$\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|$

$\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}$

$\Rightarrow t}=1,892,147.588$ years

There will be one person for every square yard of land after 1,892,147.588 years.

7 0

3 years ago

HELP NEEDED!!! WILL MARK BRAINLIEST!!!

erma4kov [3.2K]

Answer:

$x(x + 1)$

Step-by-step explanation:

$\frac{2x + 1}{ \frac{1}{x} + \frac{1}{x + 1} }$

Make denominators same:

$\frac{2x + 1}{ \frac{x + 1}{x(x + 1)} + \frac{x}{(x + 1)} }$

Add the numerators:

$\frac{2x + 1}{ \frac{x + 1 + x}{x(x + 1)} }$

$\frac{2x + 1}{\frac{2x + 1}{x(x + 1)} }$

Apply the rule:

$\frac{a}{ \frac{b}{c} } = \frac{a \times c}{b}$

Therefore,

$\frac{(2x + 1)\times x(x + 1))}{2x + 1}$

Cancel out common factor of 2x+1:

$x(x + 1)$

6 0

3 years ago

-17+4a Please solve.

ikadub [295]

Answer:

-17+4a=0

-17= -4a(-,-=+)

a=17/4

7 0

2 years ago

Read 2 more answers

What is the value if 3^0

stira [4]

3^0 if zero is an exponent then the answer would be 1.

8 0

3 years ago