Let f(x) = Vx +7 and g(x) = x +3 a) Find (2) (2) show work. b) Give the domain of the function (-) x) in interval notation

Q: Find f. - Vi- () -- 8. f'(x) = 9 %3D V1-x2 f(x)

A:

Q: Use the second order derivative test to find local exterma of the function  f(x) =x3-9x2-48x+72 on…

A:

Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

A:

Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]

Q: Determine the maximum value of the function f(x)=2sinxcosx on the interval [0, π]

A:

Q: Find the constant a such that the function is continuous on the entire real line. Ax) = {2x2, (ах -…

A: Given that , the functionfx=2x2,x≥1ax-7,x<1We have to find constant a such that the function is…

Q: Show that the functi on When x g 0 f(x)= +1 0 . When x = 0 is discontinuous at x = 0.

A:

Q: Vx + 2 Determine where f(x) = is continuous. In(3x – 5)

A:

Q: Find the points of discontinuity of the function f(x)={1−x2,x<0x+2,x≥0 if they exist.

A:

Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: Show that f(z) = 3z2 + 2z + 5 is analytic function.

A:

Q: Let f(x)=x+(1-x)^(1/2). Find the local maximum and minimum values of f using both the first and…

A:

Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: use the first derivative test to characterize each critical value of f(x)=x3+6x2-18x+3 as a maximum,…

A:

Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

A:

Q: Let f(x) = x³ + 3x2 + x + 3. Determine the points f where the tangent line is horizontal on

A: to find the points where the tangent line is horizontal we have to first derivate the function and…

Q: What is the average rate of change of the functin g(x) = 2x^2 -9 on the interval [4,7]

A: g(x)=2x2-9 on the interval [4,7]

Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

A:

Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

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

Q: (B) The function f(x) = x² + x +1 has no fixed point, prove that.

A: Let X be a nonempty set and f : X → X. A point x ∈ X is a fixed point of  f, if f(x) =x.  If no…

Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

A:

Q: Find the absolute maximum value of f(x) = x2 – 2x + 10 over the interval 0, 3 -

A: Find your answer below

Q: Obtain the ROOT of the f(x)=x²-2e-×+e-2x function using

A: b. Newton Rapshon method  fx=x2-2e-x+e-2x f'x=2x+2e-x-2e-2x , x0=4 1st iteration…

Q: Verify Mean value theorem for the function f(x)=4x3+x+2 over t interval [0,1].

A: Prove hypothesis of mean value theorem Differentiate continuous and value of c

Q: Show that f(x) = x – cos(x) has only 1 real zero on the interval [0, .

A: given fx=x-cosxx∈0,π2

Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

A:

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: Find the absolute maximum and minimum assuming the function is f(x) = 2x^4 - 8x + 3 on interval…

A: f(x)=2x4-8x+3

Q: 8. Determine the natural domain of the function Vx–1 f (x)= x²-3x+2 in interval notation.

A:

Q: Locate the absolute extrema of the function on the closed interval. f(x)= x³ 12x, [0, 4] -

A:

Q: Suppose f is a f(8(x))=2x² and differentiable function where 2x f'(x)=2+ f (x). Show that g'(x)=…

A:

Q: Verify Mean value theorem for the function f(x)=4x^3 over the interval  [0, 2].

A:

Q: Find the absolute maximum of f(x) = x³ – 12x + 1 on the interval [0, 4]. -

A:

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

A:

Q: Give an example of a derivable function f (x) with f ′ (- 4) = -3

A:

Q: 5. Use the second derivative test to determine whether f (x) = x3 – 9x2 + 24x +5 has a local maximum…

A:

Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

A:

Q: Find the specific that h (-3) =7 function satisfies hlx)こ 6-5x+x and

A:

Q: 46. Let f(x) = x³ - 4x² . Find the points on the graph of f where the tangent %3D line is…

A: 46. The given function is fx=x3-4x2. Differentiate fx with respect to x. f'x=ddxx3-4x2=3x2-8x Now,…

Q: How should the function f(x)=x²-25/x+5 be defined at -5 to make it continuous at -5?

A:

Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x<1 Here given that function is continuous…

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

A:

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: What is the largest interval in the function f(x) = x² - 2x + 1? A. (-∞, 1) B. (-∞, 0) C. (1, ∞)…

A: Function -  parabolic function    Option A is the correct option.

Q: 9. Discuss the continuity of the function x 2 x2,

A:

Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

A:

Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

A: