Given this graph of y = f(t): 4+ -1 5 -1 -2 -3 A(x) = | f(t) dt then: A(3) = A'(3) to 2.

Q: (x² + y²)dx – xydy = 0 -

A:

Q: 11. (1– e'y) dt +- dy = 0, y(1) = 1

A:

Q: A point is moving along the graph of a given function such that dx/dt is 3 centimeters per second.…

A:

Q: Solve the follow ing initial value problem: 3x(t2- 1)dt+ (t³ + 8x- 3t)dx= 0, t(0)= 1

A:

Q: A new type of bacteria is found in a sample of food. Suppose P(t) denotes the population size of the…

A:

Q: use Separation of Variables to find the general solution. dx/dt= (t + 1)(x2 + 1)

A:

Q: Find the general solution of

A:

Q: 3. If 2 = x² – x* + 6x – 5, then dty evaluated at x = 1 is dx4 dx (А) 8 (B) 36 (C) 96 (D) 120

A: To calculate the nth derivative of function y, differentiate y four times with respect to…

Q: Find the function f(x) described by the given initial value problem. F'(x)=sin x , f(0)=-3

A:

Q: 16. Suppose the radius r, height h, and volume V of a dh related to dt dV cylinder are functions of…

A: Given: A cylinder with radius, r and height, h. The formula for the volume (V) of the cylinder is…

Q: Solve the following initial value problem (t2-22t+105)(dy/dt)=y with y(11)=1 Find y as a function of…

A: According to the given information it is required to solve the given initial value problem:

Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

A:

Q: Solve the initial-value problem for y as a function of x. (16 – x)- dy = 1, y(0) = 5 dx ((1 - D- -…

A:

Q: Show that the solution of the equation dx/dt=-x(k^2+x^2) With initial condition…

A:

Q: If the equilibrium of dy/dx = y - sqrt(y) when y>0 is y=1, is it a stable or unstable equilibrium?

A: Given dydx=y−y, when y>0 We have to check whether y=1 is stable or unstable equilibrium. Note:-…

Q: If g(x) = - [e' - In(2t+1)]dt, find g''(x) . dx A e* -In(2x+1) 4 B (2x + 1)² 4 C (2x + 1)² 2 D (2x +…

A: To solve the following problem

Q: Find the general solution of the logistic equation *- » dy dt = 3y (1 -) n find the particular…

A:

Q: If x =t-1+5 and y 6+t-2 then dy at t = dx is

A: topic - derivatives answer is 4

Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: Solve the following initial value problem: dy dt - 3y + 21 y (0) = 10 y(t) =

A: The general solution of a differential equation always contains a constant of integration. The…

Q: can i get step by step help please

A:

Q: An equation that considers both the above assumptions is dP P kP(1 M - dt

A:

Q: Solve the following initial value problem. dy 1 --X, x> 0; y(6) = 3 dx x2

A:

Q: If the function f (x) solves the initial value problem dy = (x + 1)-1/2 – r dx - T. cos(T2) y(3) = 2…

A:

Q: 1 So 2t en + e-2t ezt - e-at dt

A:

Q: Find the function which solves the initial value problem dy/dx=2x−2, y(2)=−7 y(x)=?

A: The solution is:

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

A:

Q: I(x) = /, (In(t))² e-(t-1)* dt - 3x

A:

Q: Find the differential dy. y = (x+4)/(x-4)

A:

Q: Solve the initial value problem. Express y explicitly in terms of t. dy t = dt y (1 + f²) y(1) = -2

A:

Q: If y is a function of x, then the equation (y - a)dx + 3ry dy = 0 is not linear + but both + and…

A:

Q: (1² +21) dx dt = = 2x + 2 (t, x > 0), x(1) = 1

A: Given that: t2+2tdxdt=2x+2 ; x(1)=1. Find the solution of this initial value problem.

Q: Find an explicit solution of the given initial-value problem. () - 1 dx 3(x2 + 1), dt X =

A: Given query is to find the solution of the differential equation.

Q: 3. Use the phase plot for dy g(y) to identify the equilibria (if any) and their dt corresponding…

A: Step:-1 Given that dydt =gy and graph is Using above graph, we can see the graph touches and cuts…

Q: A particle moves along the x-axis so that at time t >0 its position is given by r(t) = t - 7t + 13.…

A: Given: t≥0xt=t2-7t+13

Q: Aparticle moves on the graph of y^2=x+1 so that dx/dt=4x+4 what is dy/dt whrn x=8?

A:

Q: -2 2 dx dt -12 8 with the initial value -2 x(0) = -5 x(t) =

A:

Q: Find the solution of the initial value problem subject to the indicated initial condition in terms…

A: Given 2x (x2+y)dx = d y , y(0) = -1

Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2

A:

Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x > 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: dx = x(x 1)(x + 1) dt has a solution that is

A:

Q: Solve the initial value problems for x as a functionof t. (t2 - 3t + 2) dx/dt = 1 (t > 2), x(3) =…

A: Solution: Consider the given initial value problem is t2-3t+2dxdt = 1  (t>2) Now, separating the…

Q: Q3: Consider the initial value problem. dy d²y dy dt? + 0.25y = 0 dt (0) = b. dt y(0) = 2, %3D %3D…

A:

Q: solve the bernoulli equation dx +1x' + = 0 +tx dt

A:

Q: Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у —…

A: Given that, dxdt=357-3xy-3xdydt=x2y-13xy-68y The equilibrium points are,…

Q: Solve the initial-value problem for y as a function of x. (25−x^2)dy/dx=1, y(0)=9 y=?

A:

Q: If x^2+y^2=25 and dx/dt=6, find dy/dt when y is positive and (a) x=0: x=1 x=4

A:

Q: Solve the initial-value problem for y as a function of x. (x^2+36)dy/dx=1,y(6)=0

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.