6. [T3] Prove the function f (x) = x³ – 5x² + 8x – 4 has an order two root at x=2, without using guess and check.

Q: let f(x)=ex for 0 < x < 1 Approximate f(0.25) using linear interpolation with x0=0  and x1=0.5 .…

A: Substitute x0=0 and x1=0.5 in fx=ex  and calculate L0(x) and L1(x), to construct the Lagrange…

Q: e^x=3-2x

A: Given; ex=3-2x,(0,1)

Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

A: Solution: Consider the given function is  f(x) = x8-e14x    x&lt;014x-1       x≥0 To check whether…

Q: Q5: a- Use two segment trapezoidal rule to integrate the following function numerically: f(x) =…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: The function f(x) = 2x – 42x + 270x – 2 has two critical nu The smaller one is x = and the larger…

A:

Q: For what value(s) of x is the function f(x) = } 2x + 4 (x² +x +1 if – 2 sxs1 if x>1 NOT continuous?

A:

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: Let f(x)= x2 − 6. Prove that the root of this function is equal to √6 {correct to 2 dp}, and lays…

A:

Q: For which x value does f (x) = x - 3x2 + 1have a local maximum. CO C-1 C 1 C -2 C 2

A: Given: The function fx=x3-3x2+1, To find: point of Local maximum

Q: on f(x, y) = 3x + 9y subject to th %3D

A:

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

A:

Q: 1) Find the absolute extremum values of f(x) = x² [1, 2]. – 2x + 12 over the interval

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Q: 2. Find the linearization L(x) of f(x) = x³ - 2x + 3 at x = 2 and use it to approximate f(1.9) and…

A:

Q: 22--15 if r#3 Find the value of the constant k that 5. f(x) = makes the function f(x) continuous.…

A:

Q: Show that f (x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive…

A:

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 12 over the interval [1, 3].

A:

Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: 7) Find the absolute maximum of the function f on (0,E) S(x)= 10xe

A:

Q: 2) Consider the piecewise function: |x – 1| x² – 1' x 1 For what real number A is the function…

A: A function f(x) is continuous at x=a if the left-hand limit and the right-hand limit of the function…

Q: 2. Find the critical point in the domain of following functions 2 (a) f(x) = v9 – x² (b) f(x) = x +…

A: As per company guideline we are suppose to answer only one question with three subpart at a time .…

Q: Calculate the  M6  approximation for  f(x) = 4(x + 18)  on  [5, 8].   M6 =

A:

Q: Answer the following questions for the function f(z) = zVr² + 36 defined on the interval [-7,5]. a.)…

A:

Q: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

Q: The absolute maximum of f(x) =x² – 4x on [0,3] is y= OA. OB. 4- o 3- OC. OD. 0.

A:

Q: Find the best quadratic approximation to f on the interval [ 0, 1].                     f(x) = x3

A:

Q: 4. At what value(s) of x is the function x + 2 x2 for x 1 f(x) = 3- x discontinuous?

A:

Q: Find the best quadratic approximation to f on the interval [ -1, 1].                     f(x) = lxl

A:

Q: Find the dérivative of the function: f(x)=In(e^x-13x)

A:

Q: 24, Find the domain of H function fw =J 2x+3 -1

A: Given,

Q: 5. Suppose the function g is defined by g(z) = { kz+1 for 0 < x< 3 for 3 <r < 5, mx + 2 where k and…

A: Given function is g(x)=kx+1  ,0≤x≤3mx+2 , 3&lt;x≤5 limx→3-f(x)=limx→3-kx+1=2k…

Q: 212 – 9z +4 - Let f(z) %3D 3z2 + 7z +2 This function has: 1) Ay intercept at the point 2) x…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: 1) Find the absolute extremum values of f(x) = x2 – 4x + 18 over the interval [1, 4]. [2 marks]

A:

Q: If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

A:

Q: Use the linearization of f(x) 1 at x = 4 to approximate f(4.3) . - f(x) =

A:

Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

A:

Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

A:

Q: of of and Find dy for the following function. f(x,y) 3 е 4xу In (6у) of of II

A: If the function is a multi-variable function then to find the derivative with respect to one…

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

A:

Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

A:

Q: function, that is 0 everywhere except at t=0, is know as:

A:

Q: 11. Suppose that f'(x) = Vx² + 5 and f(2) = -4. (a) Use the linear approximation of f at x = 2 to…

A: The given question can be solved as shown in step2.

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8