MATHEMATICS COLLEGE

2. From the definition of the derivative (definition 5.3), find the derivative for each of the following functions: (a) f(x) = 6x (b) f(x) = 12x – 2 (c) f(x) = kx² for k a constant

Answers

Answer 1

Answer:

Answer:

a) $f'(x)=6$

b) $f'(x)=12$

c) $f'(x)=2kx$

Step-by-step explanation:

To find : From the definition of the derivative find the derivative for each of the following functions ?

Solution :

Definition of the derivative is

$f'(x)= \lim_(h \to 0)((f(x+h)-f(x))/(h))$

Applying in the functions,

a) $f(x)=6x$

$f'(x)= \lim_(h \to 0)((6(x+h)-6x)/(h))$

$f'(x)= \lim_(h \to 0)((6x+6h-6x)/(h))$

$f'(x)= \lim_(h \to 0)((6h)/(h))$

$f'(x)=6$

b) $f(x)=12x-2$

$f'(x)= \lim_(h \to 0)((12(x+h)-2-(12x-2))/(h))$

$f'(x)= \lim_(h \to 0)((12x+12h-2-12x+2)/(h))$

$f'(x)= \lim_(h \to 0)((12h)/(h))$

$f'(x)=12$

c) $f(x)=kx^2$ for k a constant

$f'(x)= \lim_(h \to 0)((k(x+h)^2-kx^2)/(h))$

$f'(x)= \lim_(h \to 0)((k(x^2+h^2+2xh-kx^2))/(h))$

$f'(x)= \lim_(h \to 0)((kx^2+kh^2+2kxh-kx^2)/(h))$

$f'(x)= \lim_(h \to 0)((h(kh+2kx))/(h))$

$f'(x)= \lim_(h \to 0)(kh+2kx)$

$f'(x)=2kx$

Related Questions

What is the y-intercept of a line that has a slope of -3 and passes through point (-5, 4)?О-17О-11O-7O-19
Determine the level of measurement of the variable. an officer's rank in the military Group of answer choices
Rick and Tom rented party halls. The Celebrations party hall charged Rick a rental fee of $65, including music, and $25 per guest. The Feast party hall charged Tom a rental fee of $40, $25 for music, and $25 per guest.If each of them spent the same amount of money, how many guests attended Rick and Tom's party?A. Five more guests attended Rick's party than Tom's party.B. Fifteen more guests attended Tom's party than Rick's party.C. The same number of guests attended Rick and Tom's party.D. Twenty-five more guests attended Rick's party than Tom's party.
purchased a toyota 4Runner for $25,635. promised your daughter the suv will be hers when the car is worth $10,000. according to the car dealer the suv will depreciate approximately $3,000 per year,if your daughter is currently 15 years old, how old will she be when the 4Runner will be hers.
Wesson Company sold 10,000 units of its only product in the first half of the year. If sales increase by 12% in the second half of the year, which cost will increase?

What is the circumference of a circle with a diameter of 14 cm? Approximate using pi equals 22 over 7.22 cm
44 cm
154 cm
616 cm

Answers

Answer: 154 cm is the answer

Step-by-step explanation:

Answer:

154 cm

Step-by-step explanation:

Please answer this in two minutes

Answers

Hey there! :)

Answer:

m = 1/2.

Step-by-step explanation:

Find the slope using the slope formula:

$m = \frac{\text{rise}}{\text{run}} = (y_2 - y_1)/(x_2 - x_1)$

Points on the graph we can use are:

(0, 3) and (2, 4)

Plug these into the formula:

$m = (4-3)/(2-0)$

Simplify:

$m = (1)/(2)$

Therefore, the slope is 1/2.

Answer:

1/2

Step-by-step explanation:

Rise over run solution:

choose a point and go 1 unit up and 2 to the right!

hope this helped

Help me please 10 pointsssss

Answers

(4x)^2 + (x+2)^2 = (3x+4)^2
X = -1/2 , 3

Since it’s asking for the length, X would not be negative.

RS = 4X = 4*3 = 12

Answer:

I think it may be a but I am not completely sure

Step-by-step explanation:

In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.62.(a) What is the probability of more than one death in a corps in a year?

(b) What is the probability of no deaths in a corps over 7 years?

Round your answers to four decimal places (e.g. 98.7654).

Answers

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let X = number of soldiers killed by horse kicks in 1 year.

The random variable $X\sim Poisson(\lambda = 0.62)$ .

The probability function of a Poisson distribution is:

$P(X=x)=(e^(-\lambda)\lambda^(x))/(x!);\ x=0,1,2,...$

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

= 1 - P (X = 0) - P (X = 1)

$=1-(e^(-0.62)(0.62)^(0))/(0!)-(e^(-0.62)(0.62)^(1))/(1!)\n=1-0.54335-0.33144\n=0.12521\n\approx0.1252$

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: $\lambda=7*0.62=4.34$

Compute the probability of no deaths in a corps over 7 years as follows:

$P(X=0)=(e^(-4.34)(4.34)^(0))/(0!)=0.01304\approx0.0130$

Thus, the probability of no deaths in a corps over 7 years is 0.0130.

Five thirds divided by seven thirds can be solved using which of the following

Answers

Answer: 5/7

Step-by-step explanation: 5x3 = 15 and 3x7=21 , if u simplify it equals to 0.7143 and that is 5/7

Interest centers around the life of an electronic component. Let A be the event that the component fails a particular test and B be the event that the component displays strain but does not actually fail. Event A occurs with probability 0.39, and event B occurs with probability 0.24. A) What is the probability that the component does not fail the test?
B) What is the probability that a component works perfectly well (i.e., neither displays strain nor fails the test)?
C) What is the probability that the component either fails or shows strain in the test?

Answers

Answer: a. 0.61

b. 0.37

c. 0.63

Step-by-step explanation:

From the question,

P(A) = 0.39 and P(B) = 0.24

P(success) + P( failure) = 1

A) What is the probability that the component does not fail the test?

Since A is the event that the component fails a particular test, the probability that the component does not fail the test will be P(success). This will be:

= 1 - P(A)

= 1 - 0.39

= 0.61

B) What is the probability that a component works perfectly well (i.e., neither displays strain nor fails the test)?

This will be the probability that the component does not fail the test minus the event that the component displays strain but does not actually fail. This will be:

= [1 - P(A)] - P(B)

= 0.61 - 0.24

= 0.37

C) What is the probability that the component either fails or shows strain in the test?

This will simply be:

= 1 - P(probability that a component works perfectly well)

= 1 - 0.37

= 0.63

Other Questions

An island has a popularity of 1500 and is growing at a rate of 3% per year. what will the popularity be after 6 years?Ans:1791

Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg). Heavier cars tend to have lower fuel efficiencies (lower mpg ratings). Which variable (weight or fuel efficiency) is most naturally considered the explanatory (predictor) variable in this context? A. Weight B. Fuel efficiency

How many times does 4 go into 55

Simplify i^15. (imaginary numbers to the 15th power)