6. Given the functions y = f(x) and y = g(x), determine () (2) and determine the domain and range of the function (2).

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: B- Find the local extreme points of the function f(x, y) = 4xy - x - y^.

A:

Q: The graph of the linear function f(x) passes through the point (x, y) = (1, m), where m is the slope…

A: Given:Graph of f(x) passes through the point (x, y) = (1, m), where m is the slope of the line.

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

A:

Q: 2a. Which is the "upper" curve O f(x) O g(x)

A: Solution:

Q: Consider the functions :  f(x)=√x and g(x)=x-1 Solve for- (f°g) (x)

A: Given:

Q: (b) Determine the domains and range of this function: y = v1 -x-

A: The given function is y=1-x2 the domain of the function is -1≤x≤1 In the interval notation the…

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

A:

Q: 2 The function f(x) is linear and it decreases for all values of x. On the coordinate plane, draw a…

A: We want to find a decreasing linear function.

Q: What is the slope of the curve corresponding to the ff. function at the point (-3, 9/2) 1= 2²-₂ y O…

A:

Q: Find an equation for the level curve of the function f(x,y) that passes through the given point.…

A:

Q: Find the the stationary points and the local extreme values of the function f(x, y) = −2x/x2 + y2+1

A: The objective is to find the stationary points and the local extreme values for the function…

Q: Locate the discontinuities of the function. 2 f(x) = 1 + e7/x

A:

Q: The graph of f(x) passes through the point (-1,4), The slope of the line tangent to the graph at the…

A: The slope of the tangent of the function at a point is given by the derivative of the function at…

Q: 1. What does it mean to say that the equation +y 6ry defines y as an implicit function of r? %3|

A:

Q: The function f is defined by f(x) = \25 – x² for -5 sx 5. (a) Find f'(x). (b) Write an equation for…

A: Given: fx=25-x2; x∈-5,5 we know that for finding derivative of given function, we differentiate…

Q: f the total revenue function for a blender is R(x) = 76x – 0.01x² where x is the number of units…

A: Given that

Q: For the function g(x) = x², the average rate of change for the interval [-1, 3] is: For the function…

A: Here we have to find average rate of change of function.  The given function is g(x)=x2

Q: Find k such that the line is tangent to the graph of the function.…

A: To Determine: Find k such that the line is tangent to the graph of the function.…

Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: The number of deaths N per week has been observed to be linearly related to the average…

A: Given :          The number of deaths N per week has been observed to be linearly related to the…

Q: 7) Find the difference auotient. f(x+h)-f(x) for the function, f(x) = x² + 3x - 4.

A:

Q: 2. Find the domain and range of the function y = Vx + 4

A: We Know that  Domain: The set of all points over which a function is defined. Range: The set of…

Q: what is the slope of the curve

A:

Q: 4. a) Find the value of x where the function f(x) = (x – 4)5 is not differentiable.

A:

Q: How can you display the values of a function ƒ(x, y) of two in-dependent variables graphically? How…

A: For a  function ƒ(x, y) of two in-dependent variables. It can be plotted graphed using 3d plotting…

Q: 16. Find the range of the function y = 1+ x2

A: Range: The range of the function is the set of all values of the dependent variable y corresponding…

Q: From now on consider the function f(x, y) = e$n(x) y.

A: direction of fastest increase is along the gradient vector  Given f(x,y)=esinx y

Q: dont understand the fourth and fifth row of equation of gh(x) and why the function is invalid?

A: Solution

Q: Find the extreme values of the function x²y with respect to x + y = 5

A:

Q: 1 For what value of x does the function g(x) =x³ – 2x² concave downward? %3D

A: Consider the function  gx=13x3−2x2

Q: if i have the function how would i use FTC(1) and the chain rule to find g'(x)

A:

Q: 8. 4 2

A: In this question we will use basic of calculus i.e use of tangent function. We will write the…

Q: How do you find the domain and range for f(x,y) = ln(x+y)?

A: The given function:

Q: find all possible functions with the givenderivative. y' = -1/x2

A: Given: y'=1x2

Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = V f(x), evaluate…

A: To find: The value of g'(4) if g(x)=f(x). Concept used: Chain rule: f(g(x)=f'(x)g'(x)

Q: Find and classify the extreme point of the function f(x, y) 3y2x + x³ - 3y3 - 3x? + 2.

A:

Q: 6- For the function y=lnx a- Describe what type of function it is. b- How is the function related to…

A:

Q: Suppose that f is a linear function with slope 4 and that f(2) = 7. Find the equation for f with…

A:

Q: 1. What linear function,  y has f(0) = 8 and  f(7) = 14?

A: Linear function

Q: The derivative of a function is g'(x) = 19 – 6x² and the graph of g(x) passes through the point P(3,…

A: To find  g(x)

Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

A: Point of diminishing return is the point where d2Rdx2=0

Q: Find the following characteristics about the linear function 2 f(x) = ²/x + 18 x-intercept:…

A:

Q: Find the equation of the function f whoseg 3 f'(x) = (0, 4) %3D -- 1 + e

A:

Q: 8. The y-intercept is -4. The function has no x--00, f(x) → -0∞, x-intercepts. As x→ 0, f(x) → -∞…

A: 8.  The y-intercept is -4.   The function has no x-intercepts.  As x→∞, f(x)→-∞ and as x→-∞, f(x)→-∞

Q: y is a linear function of x with slope −4. If y is −3 when x is −1, what is y when x is 8? You do…

A: Linear Function  Y= mX+c  m= slope of function  c = Y intercept

Q: 2. f(x) = 6x - 1 slope: of f = of g y-intercept: of f= of g=

A:

Q: 3. Given the function g(x) = x - 2x2 + x, find the interval(s) when g is concave up and decreasing…

A: We have given a function g(x).  We have to find the interval where g is concave up and decreasing at…

Q: 19. Given the following functions: y = 8x – x2 and y = 3x %3D | Find their points of intersection.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.