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
111 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 area of a triangle with base length 8 units and height 12 units?
+
Math Question: What is the value of x if log(x) + log(2x) = log(100)?
+
What is the result of dividing 5/8 by 3/4?
+
New questions in Mathematics
A sample is chosen from a population with y = 46, and a treatment is then administered to the sample. After treatment, the sample mean is M = 47 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?
12-6x=4x+2
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
How many percent is one second out a 24 hour?
Find the measures of the sides of ∆KPL and classify each triangle by its sides k (-2,-6), p (-4,0), l (3,-1)
There are four times as many roses as tulips in Claire’s garden. Claire picked half of the number of roses and 140 roses were left in the garden. How many roses and tulips were in the Garden the first?
A study reports the following final notation: F (3, 32) = 9.50, p < .05. How many total participants were involved in this study? Group of answer choices 34 32 36
Solve : 15/16 divide 12/8 =x/y
find f(x) for f'(x)=3x+7
Is -11/8 greater than or less than -1.37?
Scores are normally distributed with a mean of 25 and standard deviation of 5. Find the probability that sixteen randomly selected students have a mean score that is less than 24.
There are 3 orchards, a, b and c. Orchard a has 60 fewer trees than orchard b orchard c has 3 times as many trees as orchard b. If the three orchards have 430 trees altogether, how many trees does orchard c have?
9.25=2pi r solve for r
Determine the Linear function whose graph passes through the points (6, -2) and has slope 3.
Associate each 2nd degree equation with its respective roots. A) x2+6x+8=0 B)x2-5x-6=0
The mean of 4 numbers is 5 and the mean of 3 different numbers is 12. What is the mean of the 7 numbers together? Produce an algebraic solution. Guess and check is acceptable.
To paint a 250 m wall, a number of workers were employed. If the wall were 30 m longer, 9 more workers would be needed. How many were employed at the beginning?
The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?
Define excel and why we use it?
f(r) = 1/r+9 find f(x^2) + 1