Consider the differential equation dy/dx = 1 + (y^2/ x).
Let y = g(x) be the particular solution to the differential equation dy/ dx = 1 + (y^2/ x) with initial condition g(4) = 2. Does g have a relative minimum, a relative maximum, or neither at ? Justify your answer.
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

Well where is dy/dx = 0 ? (horizontal either max or min or inflection)
dy/dx = 1 + (y^2/ x) = 0
or y^2 = x
It said start at (2, 4)
well that very spot is horizontal 4 = 2^2
now is it a min or a max there?
what is d^2y/dx^2 ? at (2,4) ?
dy/dx = 1 + (y^2/ x)
d/dx(dy/x) = 0 + d/dx(y^2/x)= [x(2y dy/dx) y^2] /x^2
at (2,4)= [ 2*8* (0 at that point)  16 ] / 4 = 32/4 oh that is a maximum because headed down
Answer this Question
Related Questions

math
The population of a bacteria culture increases at the rate of 3 times the square root of the present population. A. Model the population P = P(t) of the bacteria population with a differential equation. B. Solve the differential equation that models the
 asked by lovejoy

Calculus
Find the general solution for the differential equation. Leave your solution in implicit form. dx/dt=(2x)sqrt(1x)
 asked by Anonymous

AP Calc Help!!
Let f be the function satisfying f'(x)=x√(f(x)) for all real numbers x, where f(3)=25. 1. Find f''(3). 2. Write an expression for y=f(x) by solving the differential equation dy/dx=x√y with the initial condition f(3)=25. Please show work and reasoning.
 asked by Jess

Calculus
A chemical reaction proceeds in such a way that after the first second, the amount of a certain chemical involved in the reaction changes at a rate that’s inversely proportional to the product of the mass of the chemical present (in grams) and the time
 asked by Sarah

Maths
The slope of a curve is equal to y divided by 4 more than x2 at any point (x, y) on the curve. A. Find a differential equation describing this curve. B. Solve the differential equation from part A. C. Suppose it’s known that as x goes to infinity on the
 asked by axolotl

Calculus
The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = .022m, where m is the mass of the isotope in mg and t is the time in years. A. If
 asked by Anonymous

Calculus
The velocity of a particle on the xaxis is given by the differential equation dx/ dt= t^2/ 2 and the particle is at x = 4 when t = 2. The position of the particle as a function of time is: A. x(t) = t^3 / 6  26/3 B. x(t) =t +2 C. r(t) = t  2 D. x(t) =
 asked by John

Calculus/Math
The slope field for a differential equation is shown in the figure. Determine the general solution of this equation. The slope field has positive slopes in quadrants 2 and 4 and negative slopes in quadrants 1 and 4. It looks like a circle and at (0,0) it
 asked by Jojo

math
For what values of r does the function y = erx satisfy the differential equation y'' − 6y' + 3y = 0?
 asked by Sara

Calc
Consider the differential equation dy/dx=2x/y Find the particular solution y =f(x) to the given differential equation with the initial condition f(1) = 1
 asked by T

math
Write and solve the differential equation that models the verbal statement. The rate of change of N is proportional to N. (Use k for the proportionality constant.) dN dt = N(t) = I mainly need help with the bottom part below this sentence. Evaluate the
 asked by Anonymous

Calc 2
Find the solution of the differential equation that satisfies the given initial condition. dy/dx= x/y, y(0) = −7
 asked by TayB

Calculus  HELP URGENT PLEASE
Consider a lake of constant volume 12200 km^3, which at time t contains an amount y(t) tons of pollutant evenly distributed throughout the lake with a concentration y(t)/12200 tons/km^3. assume that fresh water enters the lake at a rate of 67.1 km^3/yr,
 asked by Ashley

Calculus
Which of the following is a separable, firstorder differential equation? A) dy/dx= x+y/2x B) dy/dx=x+y/xy C) dy/dx=sinx
 asked by Samantha

AP Calculus Help Five Questions
1. Find the particular solution to y " = 2sin(x) given the general solution y = 2sin(x) + Ax + B and the initial conditions y(pi/2) = 0 and y'(pi/2) = 2. 2. What function is a solution to the differential equation y '  y = 0? 3. If dy/dx = cos^2(pi*y/4)
 asked by Tom

Calculus
Suppose that we use Euler's method to approximate the solution to the differential equation 𝑑𝑦/𝑑𝑥=𝑥^4/𝑦 𝑦(0.1)=1 Let 𝑓(𝑥,𝑦)=𝑥^4/𝑦. We let 𝑥0=0.1 and 𝑦0=1 and pick a step size ℎ=0.2. Euler's method is the the
 asked by FECK

Calculus
The general solution to the differential equation dy/dx=xy is y=±√(x^2+C). Let y=f(x) be the particular solution to the differential equation with the initial condition f(−5)=−4. What is an expression for f(x) and its domain?
 asked by Carrie

Calculus
These are all the questions I missed on my practice quizzes, however I was never given the correct answers. I was hoping someone could give me the answers to these so I'd be able to study them! (I know some of them were simple/dumb mistakes :')) 1. Which
 asked by Mary

Differential Equations
Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when t0 [Hint: you need to
 asked by Erica

calculus
consider the differential equation dy/dx= (y  1)/ x squared where x not = 0 a) find the particular solution y= f(x) to the differential equation with the initial condition f(2)=0 (b)for the particular solution y = F(x) described in part (a) find lim F(x)
 asked by sammy
Still need help?
You can ask a new question or browse existing questions.