1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Law Incorporation [45]
3 years ago
13

Finding an Equation of a tangent Line in Exercise, find an equation of the tangent line to the graph of the function at the give

n point.
g(x) = e^x3 , (-1,1/e)
Mathematics
1 answer:
frutty [35]3 years ago
3 0

Answer:

y=\dfrac{3x}{e}+\dfrac{4}{e}

this is the equation of the tangent at point (-1,1/e)

Step-by-step explanation:

to find the tangent line we need to find the derivative of the function g(x).

g(x) =e^{x^3}

  • we know that \frac{d}{dx}(e^{f(x)})=e^{f(x)}f'(x)

g'(x) =e^{x^{3}}(3 x^{2})

g'(x) =3 x^{2} e^{x^{3}}

this the equation of the slope of the curve at any point x and it also the slope of the tangent at any point x. hence, g'(x) can be denoted as 'm'

to find the slope at (-1,1/e) we'll use the x-coordinate of the point i.e. x = -1

m =3 (-1)^{2} e^{(-1)^{3}}\\m =3e^{-1}\\m=\dfrac{3}{e}

using the equation of line:

(y-y_1)=m(x-x_1)

we'll find the equation of the tangent line.

here (x1,y1) =(-1,1/e), and m = 3/e

(y-\dfrac{1}{e})=\dfrac{3}{e}(x+1)\\y=\dfrac{3x}{e}+\dfrac{3}{e}+\dfrac{1}{e}\\

y=\dfrac{3x}{e}+\dfrac{4}{e}

this is the equation of the tangent at point (-1,1/e)

You might be interested in
Is 25 a perfect cube?
const2013 [10]
No,it is a perfect square
6 0
3 years ago
Read 2 more answers
The Westside Bakery uses 440 pounds of sugar to make
Marta_Voda [28]

Answer:b) 0.44

Step-by-step explanation:

5 0
2 years ago
Find the quotient −40÷20.
sukhopar [10]

Answer:

-2

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
A card is drawn from a standard 52-card deck. What is the probability that the card is a red 8, given that the card is an 8?
crimeas [40]
<span>probability that the card is a red 8
=
2 out of 52 or 1 out of 26

hope it helps</span>
8 0
3 years ago
Read 2 more answers
Square ABCD is located on a coordinate plane. The coordinates for three of the vertices are listed below.
Marrrta [24]

Answer:

B'(16,14)

Step-by-step explanation:

First find the coordinates of the vertex B. The center of the square M is the midpoint of the diagonal AC. Since A(2,7) and C(8,1), the center has coordinates

M\left(\dfrac{2+8}{2},\dfrac{7+1}{2}\right)=M(5,4).

Point M is also the midpoint of the diagonal BD. Let B has coordinates (x,y), then

\dfrac{x+2}{2}=5\Rightarrow x=8,\\ \\\dfrac{y+1}{2}=4\Rightarrow y=7.

Hence, B(8,7).

Now, the dilation by a scale factor 2 with the center of dilation at the origin has the rule

(x,y)→(2x,2y).

Thus,

B(8,7)→B'(16,14).

8 0
3 years ago
Other questions:
  • A garden pond is 6 feet wide. The perimeter of the pond is 28 feet.
    5·1 answer
  • Algebra 1 solve by elimination <br> 6x-3y=30<br> 6x+y=18
    8·2 answers
  • Ine segment AB has endpoints A(–4, –10) and B(–11, –7). To find the x-coordinate of the point that divides the directed line seg
    11·2 answers
  • Which one of the following snack combinations will best satisfy a person's daily fluid requirements?
    9·1 answer
  • <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B2%7D%20%20%3D%206" id="TexFormula1" title=" \frac{x}{2} = 6" alt=" \frac{
    8·1 answer
  • $240 was shared in the ratio of 2:3:1 by Jacob,
    6·1 answer
  • The coordinates of the vertices of ∆LMN are L(3, 0), M(2, -3), and N(0, 3).
    5·1 answer
  • What is the LCM for (x + 3)2(x – 2) and (x + 3)(x2 – 16)?
    5·1 answer
  • Which expression is equivalent to - x/y
    8·1 answer
  • How many ways are possible to select a president and vice president from an
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!