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3 years ago

5

Let the function f be continuous and differentiable for all x. Suppose you are given that f(−1)=−3, and that f'(x) for all value

s of x. Use the Mean Value Theorem to determine the largest possible value of f(5).

1 answer:

Monica [59]3 years ago

8 0

Answer:

Step-by-step explanation:

By MVT,

$f'(c) = \frac{f(5)-f(-1)}{5-1}$

$4f'(c)= f(5) + 3\rightarrow f(5) = 4f'(c) - 3$

Moreover, $f'(x)\leq 4~~~~~~ \forall x,$

$f(5) \leq 16 - 3 =13$

Hence the largest possible value of f(5) is 13

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Answer:

6 units

Step-by-step explanation:

because since AC is 24 units long, and BC is half of AC, then that would be 12 units, and since DC is half of BC, then that would be six units.

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3 years ago

Which point would be a solution to the system of linear inequalities ?

brilliants [131]

Answer:

(12,-6)

Step-by-step explanation:

we have

$y\leq \frac{4}{3}x+5$ ----> inequality A

$y\geq -\frac{5}{2}x+5$ ---> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

<u><em>Verify each point</em></u>

Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B

case 1) (0,-1)

Inequality A

$-1\leq \frac{4}{3}(0)+5$

$-1\leq5$ ----> is true

Inequality B

$-1\geq -\frac{5}{2}(0)+5$

$-1\geq 5$ ----> is not true

therefore

The ordered pair is not a solution of the system

case 2) (0,3)

Inequality A

$3\leq \frac{4}{3}(0)+5$

$3\leq5$ ----> is true

Inequality B

$3\geq -\frac{5}{2}(0)+5$

$3\geq 5$ ----> is not true

therefore

The ordered pair is not a solution of the system

case 3) (-6,-6)

Inequality A

$-6\leq \frac{4}{3}(-6)+5$

$-6\leq-3$ ----> is true

Inequality B

$-6\geq -\frac{5}{2}(-6)+5$

$-6\geq 20$ ----> is not true

therefore

The ordered pair is not a solution of the system

case 4) (12,-6)

Inequality A

$-6\leq \frac{4}{3}(12)+5$

$-6\leq21$ ----> is true

Inequality B

$-6\geq -\frac{5}{2}(12)+5$

$-6\geq -25$ ----> is true

therefore

The ordered pair is a solution of the system (makes true both inequalities)

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3 years ago

Suppose there is a 1.6°F drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on

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Answer: 55.1°F

Step-by-step explanation:

We are informed that there is a 1.6°F drop in temperature for every thousand feet that an airplane climbs into the sky, if the plane reaches an altitude of 2,000ft, the drop in temperature will be:

= 1.6° × 2

= 3.2°F

If the temperature on the ground is 58.3°F, then the temperature when the plane reaches an altitude of 2,000 ft will be:

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2 years ago

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3 years ago

Jack bought a new car in 2014 for 28,000. If the value of the car decreases by 14% each year, write an exponential model for the

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Answer:

In 2026 car will have a value of $5,000.

Step-by-step explanation:

We have been given that Jack bought a new car in 2014 for 28,000. If the value of the car decreases by 14% each year.

Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For decay or decrease b is in form (1-r), where r represents decay rate in decimal form.

Let us convert our given decay rate in decimal form.

$14\%=\frac{14}{100}=0.14$

Upon substituting a =28,000 and r=0.14 in exponential decay function we will get,

$y=28,000(1-0.14)^x$ , where x represents number of years after 2014.

Therefore, the function $y=28,000(0.86)^x$ represents the value of car x years after 2014.

To find the number of years it will take to car have the value of $5,000, we will substitute y=5,000 in our function.

$5,000=28,000(0.86)^x$

Let us divide both sides of our equation by 28,000.

$\frac{5,000}{28,000}=\frac{28,000(0.86)^x}{28,000}$

$0.1785714285714286=(0.86)^x$

Let us take natural log of both sides of our equation.

$ln(0.1785714285714286)=ln((0.86)^x)$

Using natural log property $ln(a^b)=b*ln(a)$ we will get,

$ln(0.1785714285714286)=x*ln(0.86)$

$\frac{ln(0.1785714285714286)}{ln(0.86)}=\frac{x*ln(0.86)}{ln(0.86)}$

$\frac{-1.7227665977411033893}{-0.1508228897345836}=x$

$x=11.422447\approx 12$

As in the 12th year after 2014 car will have a value of $5,000, so we will add 12 to 2014 to find the year.

$2014+12=2026$

Therefore, in 2026 car will have a value of $5,000.

6 0

3 years ago

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