2<br> Given f(x) = 3x + 10 and g(x) = x -<br> 2<br> Find the value of x when<br> g(f (x)) = -22

Find the exact location of all the relative and absolute extrema of the function. HINT [See Examples 1 and 2.] (Order your answe

icang [17]

Answer:

(-1, -32) absolute minimum
(0, 0) relative maximum
(2, -32) absolute minimum
(+∞, +∞) absolute maximum (or "no absolute maximum")

Step-by-step explanation:

There will be extremes at the ends of the domain interval, and at turning points where the first derivative is zero.

The derivative is ...

h'(t) = 24t^2 -48t = 24t(t -2)

This has zeros at t=0 and t=2, so that is where extremes will be located.

We can determine relative and absolute extrema by evaluating the function at the interval ends and at the turning points.

h(-1) = 8(-1)²(-1-3) = -32

h(0) = 8(0)(0-3) = 0

h(2) = 8(2²)(2 -3) = -32

h(∞) = 8(∞)³ = ∞

The absolute minimum is -32, found at t=-1 and at t=2. The absolute maximum is ∞, found at t→∞. The relative maximum is 0, found at t=0.

The extrema are ...

(-1, -32) absolute minimum
(0, 0) relative maximum
(2, -32) absolute minimum
(+∞, +∞) absolute maximum

_____

Normally, we would not list (∞, ∞) as being an absolute maximum, because it is not a specific value at a specific point. Rather, we might say there is no absolute maximum.

5 0

3 years ago

the production of a printer consists of the cost of raw material at 100 dollars the cost of overheads at 80$ and wages at 120$ i

Vadim26 [7]

Answer:

The percentage increase in the production cost of the printer is 3%.

Step-by-step explanation:

We are given that the production of a printer consists of the cost of raw material at 100 dollars the cost of overheads at 80$ and wages at 120$.

Also, the cost of raw materials and overheads are increased by 11% and 20% respectively while wages are decreased by 15%.

Cost of raw material = $100

Cost of overheads = $80

Cost of wages = $120

So, the total cost of the printer = $100 + $80 + $120

= $300

Now, the increase in the cost of raw material = $100 + 11% of $100

= $\$100 + (\frac{11}{100} \times \$100)$

= $100 + $11 = $111

The increase in the cost of overheads = $80 + 20% of $80

= $\$80 + (\frac{20}{100} \times \$80)$

= $80 + $16 = $96

The decrease in the cost of wages = $120 - 15% of $120

= $\$120 - (\frac{15}{100} \times \$120)$

= $120 - $18 = $102

So, the new cost of a printer = $111 + $96 + $102 = $309

Now, the percentage increase in the production cost of the printer is given by;

% increase = $\frac{\text{Net increase in the cost of printer}}{\text{Original cost of printer}} \times 100$

= $\frac{\$309- \$300}{\$300} \times 100$

= 3%

Hence, the percentage increase in the production cost of the printer is 3%.

4 0

3 years ago

Which function represents a quantity growing exponentially?

Lelechka [254]

Answer: c

Step-by-step explanation:

4 0

2 years ago

Over the three evenings,Karen received a total of 137 phone calls at the call center. The third evening, she received 4 times as

marin [14]

Answer:

1st: 22, 2nd: 27, 3rd: 88

Step-by-step explanation:

Make an equation

If she recieved x calls the 1st evening, then the 2nd evening she recieved x+5, and the 3rd evening she recieved 4x.

x+x+5+4x=137

Combine like terms

6x+5=137

Subtract 5 from both sides

6x=132

Divide by 6 on both sides

x=22

First:

22 calls

Second:

x+5

22+5

27 calls

Third:

4x

4*22

88 calls

Hope this helps!

3 0

2 years ago

Kelly solved an equation: H/ 4 - 11 = 13 using two inverse operations of adding 11 to both sides of the equations, and then divi

MariettaO [177]

Answer:

She should have multiplied by 4, not divided

Step-by-step explanation:

Given

$\frac{H}{4}$ - 11 = 13 ( add 11 to both sides ) ← correct

$\frac{H}{4}$ = 24 ( multiply both sides by 4 to clear the fraction )

H = 4 × 24 = 96

H is divided by 4, thus the inverse operation is to multiply

6 0

2 years ago

2 Given f(x) = 3x + 10 and g(x) = x - 2 Find the value of x when g(f (x)) = -22