MATHEMATICS COLLEGE

Pre Calc Introduction to Derivatives-Using Limits Help!

Answers

Answer 1

Answer:

Answer:

Attachment 1 : Option A,

Attachment 2 : Option D,

Attachment 3 : Option B,

Attachment 4 : Instantaneous rate of change will be 24

Step-by-step explanation:

"Remember that we can solve such questions by finding the derivative first"

1 : Let's consider this approach a bit differently. If we were to graph this function, we would see that the point (-2,26) would lie on the curve having a negative slope.

The rate of change would thus be negative, eliminating choices b and d. And, the slope of this function would be much greater than 4 due to the coefficient of " 5 " in f(x) = 5x² + 6. Hence our answer will be option a.

2 : f'(5) = - 2 * 5 + 4,

f'(5) = - 10 + 4 = - 6

Your solution is option d.

3 : f'(2) = 12 / 2 + 1 / - 3,

f'(2) = 12 / 3 / - 3 = 4 / - 3,

f'(2) = - 4 / 3

Your solution is option b.

4 : Here again we can apply the power rule, where using constant multiple rule and derivative of a constant, you can quickly find the derivative of g.

g'(t) = 3(2x¹) + 0 = 6t,

And now we can evaluate the derivative at that value of t.

g'(4) = 6(4) = 24 - hence the instantaneous rate of change at t = 4, will be 24

Related Questions

observe as seguintes situações e sua representação em linguagem matematica dois numeros x e y são tais 2x y=6 x-y=3
According to the graph, what is the value of the constant in the equationbelow?25+(3.25)HeightConstantWidth20 +15(5, 15)Height10(15,5)(25,3)10152025WidthO A. 5B. 100O c. 10O D. 75
The model represents an equation . What is the solution for this equation . Please help I’ll mark you as brainliest if correct
Craig Browning bakes cookies for the elementary school cookie sale. His chocolate chip cookies sell for $1.00 a dozen, and his oatmeal brownie cookies sell for $1.50 a dozen. He will bake up to 20 dozen chocolate chip cookies, and up to 40 dozen oatmeal brownie cookies, but no more than 50 dozen cookies, total. Also, the number of oatmeal brownie cookies will be no more than three times the number of chocolate chip cookies. How many of each kind should Craig make in order for the elementary school to make the most money
the gas tank on toms car holds 20 gallons of gas. The fuel gauge of her car shows that the tank is 3/4 full. How many gallons of gas are in the gas tank?

A deep-sea diver is in search of coral reefs.he finds a beautiful one at an elevation of -120 4/7feet. While taking pictures of the reef he catches sight of a manta ray. He swims up 25 3/7feet to check it out.what is the diver's new elevation?

Answers

Answer:-95 1/7 feet

Step-by-step explanation:

-120 4/7+25 3/7=-95 1/7 feet

How do you do this 6-2x=10

Answers

-2x=10-6

The answer: x= -2

Answer:

x= -2

Step-by-step explanation: (remember the 6 in this equation is positive so you'll subtract it and the 2 is actually -2x. First, you'll subtract 6 from itself and 10, the two 6's cancel out and 10-6=4. Then, you'll divide -2 and 4 by -2, the two -2's cancel out and 4 divided by -2 is -2. Finally, you'll see that x = -2. This is all done by the order of operations also known as PEMDAS. )

6 - 2x =10

-6 -6

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

-2x = 4

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

-2 = -2

x = -2

What is the system of checks and balances designed to ensure?

Answers

Answer:

ensure that no single branch of government would have too much power

Step-by-step explanation:

The side length of a square is 5 feet. A. What is the perimeter of the square? B. What is the area of the square?

Answers

Answer:

A. 20 B. 25

Step-by-step explanation:

A. Perimeter equals the all the side lengths added together, so 5+5+5+5=20

B. Area equals (for a square) two side lengths multiplied by one another, so 5x5=25

The mass of a snowflake is approximately 0.000003 kilograms. Write this number in scientific notation.

Answers

Answer:

Step-by-step explanation:

3 x 10^-6 kg

The amount of cereal in a box is normal with mean 16.5 ounces. If the packager is required to fill at least 90% of the cereal boxes with 16 or more ounces of cereal, what is the largest standard deviation for the amount of cereal in a box?

Answers

Answer:

The largest standard deviation for the amount of cereal in a box is 0.3906.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 16$

The z-score of X = 16 has a pvalue of 0.1. So it is $Z = -1.28$ . Now we have to find the value of $\sigma$ .

$Z = (X - \mu)/(\sigma)$

$-1.28 = (16 - 16.5)/(\sigma)$

$-1.28\sigma = -0.5$

$\sigma = 0.3906$

The largest standard deviation for the amount of cereal in a box is 0.3906.