1. How does the graph of f (x) = vVx – 2 differ from the graph of y = Vx+ 3 ?]

Q: What is the relative minimum value of the function f(x, y) = x³ – 3xy + y³ – 2?

A:

Q: 21. Find the quadratię function y = ax² + bx + c whose graph passes through the points (-1,0), (1,…

A:

Q: Find the length of the curve e^x / 2 + e^-x /2 between x=0 and x=1

A:

Q: 1. Sketch the graph of y = sinx,0 ≤ x ≤ 360°, and complete the table below Maximum: Minimum:…

A: This question is based on graph of y=sinx

Q: If f(x) = x – kx-1 has a relative maximum at x = -2, then the value of k is %3D

A:

Q: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

Q: Find all points (x, y) on the graph of g(x) = 1/3 x3 - 3/2 x2 + 1 withtangent lines parallel to the…

A: Given: The function gx=x33-3x22+1, To find: All the points x,y on the graph of given function at…

Q: Q1- Find any local maximum and local minimum values and sketch the curve: x? + 1 f(x) = x2. - 1

A: Given that  f(x)=(x^2+1)/(x^2-1) To find the local maximum and local minimum

Q: 1) Find a function y whose graph passes through the point (1, ) and satisfies x?y' = y.

A:

Q: Show that the function f(x) = e1/2)[(x-µ)/a}° has a relative maximum at x = µ.

A: fx=e-12x-μσ2 Differentiating with respect to x, we get…

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Given: For any function y=f(x) can be expressed as x=f(y) in standardmathematical methods for…

Q: Find the absolute maximum and absolute minimum of f(x)=e^(−2x) over the interval [−1,3].

A:

Q: 8. Find the extremum and saddle points of the function f(r, y) =r' - 3ry + y if any.

A: Due to Bartleby guidelines, only 1st question can be answered if multiple questions have been asked.…

Q: 1) Find a function y whose graph passes through the point (1, and satisfies x?y' = y.

A: We have to solve

Q: 1. Find the domain and two level curves of f(x,y) = /25 – x² – y2

A: As per guidelines, we will solve the first question only. 1. Given function is   f(x,y)=25-x2-y2

Q: At what value of x is f minimum?

A: To find: The value of x for which f is minimum. Calculation: It is observed from the graph that the…

Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1.…

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Q: Find the relative maximum or minimum value (if any) of f(x, y) = (x2 + y)ey/2

A:

Q: 3. Find the fixed point(s) of f: [1, ∞)→→ [2, ∞) defined by f(x) = √²+x.

A: 3) To find: fixed points of f:[1,∞)→[2,∞) defined as f(x)=x2+x.

Q: 5 Find the point X to minimize the function f(x1, x2) =1+¤1 +2x2+ from the strating point X, = using…

A: We are given the following optimization problem : f(x1 , x2) = 1 + x1 + 2x2 + 5/x1 + 10/x2 And we…

Q: Find the maximum and minimum values of the function f(x, y) = e²Y subject to + y° = 16

A: Given data: The expression for the first function is f(x, y)=exy. The expression for the second…

Q: f(x, y) 3xy-x² - y²

A: See the details solution in below

Q: 1. The minimum point on the graph of the equation y = f(x) is (2, – 1). If f(x) is shifted 3 units…

A: Given that y=f(x)minimum point on the graph is (2, -1)

Q: 1. Use the graph below to state the absolute and local maximum and minimum values of the function. y…

A: Explained below

Q: 2 If f(x) = 2x- kr has a relative maximum at r = -2, then the value of k is %3D

A: Note :-  If f(x) has relative maximum at x=a then f'(a) =0.

Q: (12) Find the local maximum, minimum and saddle points (if any) of the function f(x, y) = x3 – 3x +…

A: Local maximum or minimum of the function

Q: | 1) Find a function y whose graph passes through the point (1, ) and satisfies x²y' = y.

A:

Q: II- Find the local maximum and minimum values and saddle points of the 3y? 3xy - 2 function f(x, y)…

A:

Q: True or false: The minimum value of the function y = 2 sin x + 1 is -1._______

A: True or false: The minimum value of the function y=2 sin x+1 is -1.

Q: 1 Find the length of the curve f(x) + from x = 2 to x = 4. %3D 6. 2x

A:

Q: With y=c1.x2+k curves and curves x2+2.y2-y= c2 intersect perpendicularly. Where C1 and C2 are…

A: Given two curves are y=c1x2+k   and x2+2y2-y=c2  , where c1 & c2 are arbitrary constants. Let us…

Q: f(x, y) = 3xy – x²y- xy?

A:

Q: Find the value for x for which the graph of y =2e reaches its first minimum value.

A: To find the value for x for which the graph of below equation reaches its first minimum value.…

Q: At what value of x does the curve y = x(x – a²)(x – b²) have a local maximum?

A:

Q: Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes…

A:

Q: 13. Find the minimum and maximum value of the function on the given interval. y = 2x 2 + 4x + 5 [-2,…

A:

Q: Find the global maximum and global minimum of the function f(x)=x2−16x on the interval [−4,−1].

A:

Q: Find the level curve of the function at c=2 for g(x,y)=(x^3-y)

A: A scalar function g(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: 8. Determine a quadratic function f(x) = ax² + bx + c if its graph passes through the point (2,22)…

A:

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 8. Find the local maximum and minimum values and saddle points of the function f(x,y)=2x + 4y +3x²…

A: This is a problem related to maxima and minima. Please follow the procedure given below.

Q: 30. The graph of y = x³ + 21x² – x + 1 is concave down for (a) x 7 (e) x 7.

A:

Q: The value of Wronskian of two functions y, =7* and y2 =7** is

A:

Q: Consider the function y = 3x - C(In x) where C represents a constant. If this function has a local…

A: If any given function f(x) has local maxima or minima at x=a, then the point corresponding to x=a…

Q: 9. An equation of the line normal to the graph of f(x)=, at (1,–1) is (a) 2x - y -3 -0 (b) 2x + y…

A: Explanation: Given that  f(x)=xx-2 at (1,-1)   Concept Used: To find the normal firstly find the…

Q: For what values of a and b does f(x) = a(x- bln a) have a local minimum at the point (2, 5)? Figure…

A:

Q: At what x-value(s) on the interval [-2, 3] does the graph of f (x) = x² + 2x – 1 satisfy the M.V.T.?

A: According to mean value theorem,Let f be continuous on [a,b] anddifferentiable on (a,b). Then…

Q: Find the extremum and saddle points of the function f(x; y) = x^3 -3xy + y^3 if any.

A: we use second order partial derivative test to find out minimum, maximum and saddle point

Q: 1) Find a function y whose graph passes through the point (1, 2) and satisfies x?y' = y.

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.