Question

Find the equation of the tangent line to the curve of the function y=x^2 at the point P(2,4)

165

likes
827 views

Answer to a math question Find the equation of the tangent line to the curve of the function y=x^2 at the point P(2,4)

Expert avatar
Santino
4.5
102 Answers
Para encontrar la ecuación de la recta tangente a la curva de la función y = x^2 en el punto P(2, 4), necesitamos determinar la pendiente de la recta tangente y usar la forma punto-pendiente de una ecuación lineal. . La pendiente de la recta tangente en un punto dado es igual a la derivada de la función evaluada en ese punto. Para la función y = x^2, la derivada viene dada por: dy/dx = 2x Para encontrar la pendiente de la recta tangente en el punto P(2, 4), sustituimos x = 2 en la derivada: dy/dx = 2(2) = 4 Entonces, la pendiente de la recta tangente en P(2, 4) es 4. Usando la forma punto-pendiente de una ecuación lineal, que es y - y1 = m(x - x1), donde (x1, y1) es un punto en la recta y m es la pendiente, podemos sustituir los valores de P( 2, 4) y la pendiente m = 4: y - 4 = 4(x - 2) Simplificando aún más: y - 4 = 4x - 8 Finalmente, podemos reordenar la ecuación para obtener la forma estándar: y = 4x - 4 Por lo tanto, la ecuación de la recta tangente a la curva de la función y = x^2 en el punto P(2, 4) es y = 4x - 4.

Frequently asked questions (FAQs)
What is the value of sine of angle x in a right triangle, if the opposite side is 5 and the hypotenuse is 13?
+
What is the value of sin(45°) + cos(60°) - tan(30°) divided by sec(45°) multiplied by cot(60°)?
+
What is the sum of the interior angles in a right-angled triangle?
+
New questions in Mathematics
Students Ana Beatriz and Paula decided to register on a website with exercises to study for upcoming simulations, but to register on this website, they need to choose a password consisting of five characters, three numbers and two letters (capital letters). or lowercase). Letters and numbers can be in any position. They know that the alphabet is made up of twenty-six letters and that an uppercase letter differs from a lowercase letter in a password. What is the total number of possible passwords for registering on this site?
1 + 1
Convert the following function from standard form to vertex form f(x) = x^2 + 7x - 1
8x²-30x-10x²+70x=-30x+10x²-20x²
A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?
The mean temperature for july in H-town 73 degrees fahrenheit. Assuming that the distribution of temperature is normal what would the standart deviation have to be if 5% of the days in july have a temperature of at least 87 degrees?
7273736363-8
Serum cholesterol levels in men aged 18 to 24 years have a normal distribution with a mean 178.1mg/100 ml and standard deviation 40.7 mg/100 ml. The. Randomly choosing a man between 18 and 24 years old, determine the probability of your serum cholesterol level is less than 200. B. Whether a serum cholesterol level should be judged too high if it is above 7% higher, determine the value of the separation level of levels that are too high. w. Determine a 90% reference range for serum cholesterol level among men from 18 to 24 years old.
how many arrangements can be made of 4 letters chosen from the letters of the world ABSOLUTE in which the S and U appear together
A pair of die is thrown and the absolute difference of the two scores is recorded. What is the probability of the absolute difference being 4 or more?
4x/2+5x-3/6=7/8-1/4-x
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
The Humane Society has asked for our help again this week. Currently they are charging $50 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis. During a client meeting we gathered these facts. There are 2 part-time employees that each earn $1000 per month. The utilities for the kennel area (water, electricity) are $200 per month. The average food cost for animals in the kennel is $800 per month. In addition, each animal that is adopted receives a rabies vaccination that costs $4 and is micro-chipped that costs $6. At the current cost of $50, how many animals must be adopted to break-even? What would break-even be at a $60 adoption fee? What would break-even be if the fee were lowered to $40? The newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs $1000 for a very small ad run every day for a month. If the Humane Society does this extra advertising, how will it affect breakeven? Based on what you have learned about elasticity, what price do you recommend for the adoption fee?
Equine infectious anemia (EIA) is considered the main infectious disease in Brazilian equine farming, for which there is no effective vaccine or treatment. It is caused by a retrovirus of the genus Lentivirus, which affects horses, donkeys and mules and is transmitted in nature mainly by hematophagous insects of the genus Tabanidae. Researchers analyzed the records of 9,439 equids from Acre, submitted to the agar gel immunodiffusion test (AGID) for equine infectious anemia (EIA), between 1986 and 1996. Of these, 6199 tested positive for equine infectious anemia (EIA) . Knowing that the age of AIE-positive horses follows a Normal distribution with a mean of 5 years and a standard deviation of 1.5 years, determine the expected number of AIE-positive horses in the Acre sample that will be aged less than or equal to 3 years. ATTENTION: Provide the answer to exactly FOUR decimal places.
DuocUC 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function: (x+185) C(x)=81300-6x+ 20000 a) It is known that C(90) 5.344. Interpret this result. (2 points) b) Calculate C'(x) (2 points) 3 x²+111x-0.87 20000 2000 c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing. (3 points) d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost? (
Translate to an equation and solve. Let x be the unknown number: What number is 52% of 81.
x²-7x+12=0
there are 500,000 bacteria at the end of a pin point. 1000 bacteria can make a person sick. then bacteria at the tip of a pin point can make 500 people sick. Also, many people do not know that bacteria can (reproduce). Let's say there are 5 bacteria and we leave it for 15 minutes. bacteria will multiply to 10. if left for up to 30 minutes, 20 bacteria will form. if left up to 45 minutes. bacteria will multiply up to 40. every 15 minutes the bacteria will double 2. if you start with five bacteria that reproduce every 15 minutes, how manu bacteria would you have after 12 hours ?
What js the greatest 4-digit even number that can be formed by 3,6,1,4?
In a school playground When going out for recess, 80 men and 75 women coexist, the Patio measures 10 meters For 40 meters (what will be the population density in the break