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
Semmy [17]
3 years ago
15

Find the second derivative at the point (1,2), given the function below. y^2-2=2x^3

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
5 0

Solution:

Given:

y^2-2=2x^3

Lets First Differentiate the given equation with respect to x

\frac{d}{dx} ( y^2 - 2 ) =  \frac{d}{dx} 2x^3

2y \cdot \frac{dy}{dx} - 0 = 6x^2

\frac{dy}{dx} = \frac{6x^2}{2y}

\frac{dy}{dx} = \frac{3x^2}{y}-----------------------(1)

this can be rewritten as

\frac{dy}{dx} =3x^2y^{-1}

Now differentiating again with respect to x

\frac{d^2y}{dx^2} =6x^2y^{-1} +  3x^2 \cdot (-y^{-2}) \cdot \frac{dx}{dy}

Now substituting (1) we get

\frac{d^2y}{dx^2} =6x^2y^{-1} +  3x^2 \cdot (-y^{-2}) \cdot \frac{3x^2}{y}

\frac{d^2y}{dx^2} = \frac{6x^2}{y} + ( \frac{3x^2}{y^2}) \cdot \frac{3x^2}{y}

\frac{d^2y}{dx^2} = \frac{6x^2}{y} + ( \frac{9x^4}{y^3})

At(1,2) \frac{d^2y}{dx^2} = \frac{6(1)^2}{2} + ( \frac{9(1)^4}{(2)^3})

\frac{d^2y}{dx^2} = \frac{6}{2} + ( \frac{9}{8})

\frac{d^2y}{dx^2} = 3 + 1.125

\frac{d^2y}{dx^2} = 4.125

You might be interested in
Harold weighs 270 pounds now. If Harold goes on a diet and loses 30 pounds, then how many kilograms will he weigh?​
Leto [7]

Answer:

108.862 kg

Step-by-step explanation:

270lb -30lb =240 lb

240 lb is approx. 108.862 Kg

(Pounds are approx 2.205 times Kg)

<em>I hope this helps! :)</em>

3 0
3 years ago
Read 2 more answers
Two integers a and b have a product of -48
ycow [4]
It’s c because I got it right on the test
3 0
3 years ago
Solve the equation using the quadratic formula
amm1812

Answer:

Step-by-step explanation:

Rewrite this quadratic equation in standard form:  2n^2 + 3n + 54 = 0.  Identify the coefficients of the n terms:  they are 2, 3, 54.

Find the discriminant b^2 - 4ac:  It is 3^2 - 4(2)(54), or -423.  The negative sign tells us that this quadratic has two unequal, complex roots, which are:

     -(3) ± i√423        -3 ± i√423

n = ------------------- = ------------------

             2(2)                      4

3 0
3 years ago
In the diagram, AB=18. find AC and BC
LuckyWell [14K]

Answer:

b

Step-by-step explanation:

In a 30-60-90 right triangle, the hypotenuse is twice the length of the short leg.

The hypotenuse is AB and is 18.

The short leg is BC and is 9.

The only choice with BC = 9 is b.

Answer: b

3 0
2 years ago
A circle is centered on point B. Points A, C and D lie on its circumference.
Mademuasel [1]

Answer:

122

Step-by-step explanation:

61 x 2 = 122 hope this helps:)

4 0
3 years ago
Other questions:
  • This is what I've done so far but does anyone know what I do next or did I make a mistake
    6·1 answer
  • 5/6,3/8 The LCD is 2 24 48
    8·1 answer
  • A line passes through (−1, 7) and (2, 10). which answer is the equation of the line?
    7·1 answer
  • Consider the following table of the ages of our first six presidents. Ages of the First 6 Presidents at Inauguration Washington
    14·1 answer
  • At what point do the graphs of the equation 9x-2y=30 and x+2y=10 intersect?
    8·1 answer
  • How can you use a bar diagram to check<br> your solution in a ratio problem
    7·1 answer
  • Indicate a general rule for the nth term of the sequence a1 = 2 and r = √3.
    6·1 answer
  • Help me solve this plssss
    5·2 answers
  • A student must find the slope of a line that passes through the points (2.2) and (-1, 3). Which of the statements
    14·1 answer
  • The first and second terms of a linear sequence (A.p) are 3 and 8 respectively. Please determine the least Number of terms of Ap
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!