Re-arrange the equation as a function of c only.

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: Is it possible to get a example which shows this applied to a model

A: To determine: An example which shows the application of Taylor series in a model.

Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: y = x – 2 + Ce* X-

A:

Q: (D^3-2D^2-5D+6)y=e^(3x)

A:

Q: What are the maximum and minimum values in application of derivatives?

A: We have to define the maximum and minimum values in application of derivatives.

Q: Optimize the function f(x,y) = x^2+y^2 given the condition of x=y^2-5.

A: Answers are following in explanation step.Explanation:

Q: 2(p^2+q^2)=x^2+y^

A: Given,           z2(p2+q2)=x2+y2

Q: (2x^2)– (y^2)-2xC+1=0  Find the orthogonal orbital family of the function

A: We have to find the orthogonal trajectory of the function given below: 2x2-y2-2Cx+1=0. Orthogonal…

Q: Show that the functions y1= e^t,  y2 = e^-t, and te^-t are linearly independent.

A:

Q: can we calculate the derivative of a matrix and the nth root of a matrix ?

A: Yes, derivative of a matrix and the nth root of a matrix both can be calculated.

Q: The height of an adult can be predicted from their height as a child. If a child is i inches tall at…

A: Any values for i and w can be substituted in the function, H(i,w) = 150 iw to calculate the value of…

Q: What is the fxx, fyy, and fxy of f=(2x^4)+(y^2)-(x^2)-(2y)?

A:

Q: Fill in the appropriate blanks for the derivatives of the given functions, then evaluate each…

A:

Q: find |A^T| |A^2| |AA^T| |2A| |A^-1| A= [ 5. -10] [4, 6]

A: As we know that the properties of determinant: 1 A=AT2 A2=A23 AB=AB4 KA=KnA where n is the order of…

Q: The point (m,n) and (p,q) are on gra y=a^x. In term of n and q, determine coordinate of point…

A:

Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

Q: Find f if ∇f = 4xy i + (2x^2 + 8y) j

A: Here I am attaching image so that you understand each and every step.

Q: 3) A researcher has collected population data along with time. Afler comparing the populations from…

A: Solution is given below

Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: how is v^t calculated

A: In the calculation of actuarial present value of a pension that pays $50,000 per year as long as at…

Q: Which set of functions which is not linearly independent is  A-X^2,4x^3 B-2x,6x+3,3x+2 C-e^x,e^2x…

A: A set of functions will be linearly independent if there Wronskian is not equal to zero. Wronskian…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: