4. Find the domain and the range for the following functions. Then, sketch its graph. (a) :=+/8-x² - y² (b) f(x,y)= Vx² +y +8 (c) :=x +y +V8

Q: Given the function f(x) = x³ - 3x2 x – 1, determine all coordinate points (x, y) on the graph of f…

A: The derivative of the function will give the value of slope. For two value of x, f(x) will have…

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: This function has: 1) A y intercept at the point 2) x intercepts at the point(s)

A: Given,  fx=2x2+11x+123x2+10x+3 The x-intercept, y-intercept, and vertical asymptotes are to be…

Q: 7/8 For what value of x does the graph of f(x) = x8e* have a horizontal tangent?

A:

Q: 3. If y = 4v2 r x – 1, find the length of the graph of f 3 from point a = 0 to x = 1.

A:

Q: Find the length y=(x+2)^3/2 for x in the range 0≤x≤2.

A:

Q: If the critical point of the function f(x.y)-x- y- 2xy +6 is (0.0). test this point whether it is:

A: We use second order partial derivative to know about critical point behaviour

Q: Find the equation of the line that is tanget to f(x)= 1/x at the point (2,1/2).

A: We need to find the equation of the line that is tangent to f(x) = 1/x at the point (2,1/2).

Q: Find the slope of the secant line connecting the points on the graph f(x)=2h+4x-12, with the given…

A:

Q: Find the equation of the secant line on the curve f(x) = -x²+2 passing through the points xo = -1…

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: Find the slope of the secant line between x=−2 and x=3 on the graph of the function f(x)=−2x2 −5x+1.

A: The point on the graph when x =-2 is given by plugging x=-2 in the function:Hence, the point on the…

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

A: Given graph is as follows where the red graph shows f(x)  and a line tangent to the curve at x=4.…

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

A: Finding the g'(4) from the given conditions.

Q: Match the function with its graph. I II y 1 III IV (a) f(x) = x2 ---Select--- (Б) f(x) = x3…

A: use the basic concept of function and  graph we get the match.

Q: 1 For f(x) -x² + x + 2, find: a) the equation of the line that is tangent to the graph of f at the…

A:

Q: Find domain and range F(x,y)= Vx-1

A: Since you have asked multiple questions in a single request, as per policy, only the first question…

Q: For the below function, find the stationary point(s) and prove if a maximum, minimum, or a saddle…

A: The given function is fx,y=-x2+6xy+y2-10x-5y. Compute the first and second partial derivatives as…

Q: The function g is difirentiable and satisfies g(-1)=4 and g'(-1)=2. what is the approximation of…

A: given g(-1)=4 and g'(-1)=2.         g(-1.2)=?

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: 10. Find a function y = ax +bx+c whose graph has an x-intercept of 1, a y-intercept of -2, and a…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Find the intercepts of the function. f(x)-x* +2 а.

A: Given data÷

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

A:

Q: Use the graph of the function f to find approximations of the given values. y 4-

A: To find the values of f at x= a,  we imagine the vertical line x=a and where the vertical line…

Q: Find the slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=−2x3 +3.

A: Given lines are x = –1 and x = 2. Given function is

Q: am having trouble finding the equation of the line tangent to the graph of f at (1,1), where f is…

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: 4. Find the point on the graph of f(x) 5x2 + 20x – 3 where the tan gent line is horizontal. (a)…

A: We have to solve integration

Q: The graph of f(x) is given on the grid. Graph f'(x), its derivative. 05 4 -8 -7/-6 -5 -4 -3 -2 -1 I…

A:

Q: Match f(x) with its graph without using a calculator. -… (x)

A:

Q: 5. If f(x) = ax* + bx' +cx² + dx +e, determine a, b, c, d and e so that the graph of f will have a…

A: 5) Given:   f(x)=ax4+bx3+cx2+dx+e As f(x) passes through origin (0,0) then substituting (0,0) in…

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: For what value(s) of x does the graph of f(x) = 4x3 - 6x2 - 144x - 24, have a horizontal tangent?

A:

Q: 3. If y = 2 x –-1, find the length of the graph of f from point z = 0 to z = 1.

A:

Q: Find k such that the line is tangent to the graph of the function. Function= f(x) = k square root x…

A: Find k such that the line is tangent to the graph of the function. Function= f(x) = k square root…

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

A:

Q: Find the point on the graph of f(x) = Vx that is closest to the point (5, 0). (x, y) =

A: Use distance between point concept and then differentiate

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 the slope of the secant line between x=3 and x=5 on the graph of the function f(x)=−2x^2+2x+5.

A:

Q: fla)= 9 (x=4)° +2 +2

A: Given fx=9x-42+2.

Q: 8. Given the function f(x)%=2x3 -5x3 , find the point where the tangent is horizontal to the curve.

A:

Q: Find the equation of the line tangent to the graph of f(x) = 3 - 2x at x = 3. Provide your answer…

A: Given : The curve is fx=3-2x and point is x=3. To find : The equation of the line tangent to the…

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. 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: This extreme value problem has a extreme values of the function sub f(x, y) = 4x + 8y, x2 maximum…

A: Method of Lagrange's multiplier: The Lagrange multiplier method is a straightforward and elegant way…

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…

Q: Find the line tangent to the function at the indicated point: f(x) = v8x² – 4x ;x = 1 ОУ-12х-10 o…

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of g at x=3 is…

A: Given that: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of…