77. Show that if f is a quadratic polynomial, then the SDQ at x = a (for any h + 0) is equal to f'(a). Explain the graphical meaning of this result.

Q: he Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 Ciuo Hooim

A: Here we have to use linear approximation rule.

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

A:

Q: Find the local linear approximation of f(x) at 4 + x xo = 3, where Ax = x – 3. NOTE: Enter the exact…

A: f(x)=14+x

Q: What are the zeros of f(x)=2cos(3x)+1 on the interval [0,π]?

A: We have the given function as fx=2cos3x+1. In order to find the zeros of the function fx, we must…

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)

A:

Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

A:

Q: Calculate the error in using the divided differences for approximating the derivative at x 5 using a…

A: Use the Newton's divided difference interpolation formula, to obtain the equation for f(x).…

Q: 7. Is the function given by G(x) at x = 2? Why or why not? 1 x² - 6x + 8 continuous

A: Theory : If A function f(x) is continuous at some point a, then it must satisfy All of these…

Q: What is the upper bound of the function? f (x) = 4xª 25x² – 5x = 13 = 4r4 5х -13 --- Enter your…

A: Given : f(x) = 4x⁴ - 25x² - 5x - 13

Q: Use the IVT to find an interval of length ½ containing a root of f(x) = x3 + 2x + 1.

A: Intermediate Value Theorem If f is continuous on a closed interval a,b, then for every value M…

Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

A:

Q: Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6). Show all work.

A: Absolute extrema at x=2 and 6..

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: Use bisection to find the root of function f(x) = x* – 18 that lies in the interval (1.8, 2.2)…

A: Given:           f(x) = x4-18 The root of f(x) lies in the interval (1.8, 2.2) The relative…

Q: Calculate the error in using the divided differences for approximating the derivative at x 5 using a…

A: Use the following formulae, to obtain the required result. The Newton's divided difference…

Q: 92. Use the definition of the derivative to prove that every quadratic function f(x) = ax² + bx +c…

A: Consider the quadratic function: fx=ax2+bx+c. To show horizontal tangent line is at the point x=-ba.…

Q: Use the Linear Approximation to estimate Af = f(4.8) – f(5) for f(x) = x – 5x². (Use decimal…

A: Given data:   The given expression for the function is f(x)=x-5x2. The given value a=5.   The…

Q: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

A:

Q: 64. Is the function given by f(x) = continuous %3D =2- 6x + 8 at x = 3? Why or why not?

A: We have to check the given function fx=1x2-6x+8 is continuous at x=3 or not. To check the continuity…

Q: Assume that f is a polynomial and x = 10 is a critical number for f If f''(10) = -sqrt2 what do we…

A: A function y = f(x) has a critical point at (x, y) if f'(x) = 0 or f"(x) is not defined. But as we…

Q: is the net signed area between f(x)=2x+2 and the x-

A:

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

A:

Q: ) Use Taylor's formula to estimate the error in the approximation In(x) ~ P3(x) or all x in the…

A: Since you have posted multiple questions but according to guidelines we will solve the first…

Q: Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = - %3D 5+x? (Use decimal…

A: fx=115+x2,a=2;∆x=-12 Now, differentiate the function with respect to x.…

Q: Find Maclaurin polynomial for f(x) = sin(2x) when n = 5. %3D

A:

Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Find the extrema of f(x) = 3x4 − 4x3 on the interval [−1, 2].

A: The given function f(x) = 3x4 − 4x3 on the interval [−1, 2].

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show…

A: We will find out the required value.

Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: Show that the nth Maclaurin polynomial of f (x) = arcsin x for n odd is 1.3 x Tn (x) = x+ 23…

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: The 2nd approximation to the real root of the equation x³ – x² – 1 in the interval [1, 2] using…

A:

Q: At which interval of x is the function of P(x)=(sqrt(1-x^2)) discontinous?

A:

Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

A:

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of…

A: Consider the given: The Maclaurin series for sin x centered at x = 0 is:…

Q: Find Newton’s polynomial that interpolates f(x) = x1 at x = 1, x=2,x=4,andx=5.…

A: Since, function is not clear so we assume fx=1x. We have to find the Newton's polynomial that…

Q: Let f (x) = In(x + 2). Use the definition of the derivative and your now expanded knowledge of…

A:

Q: 13 Use the Linear Approximation to estimate Af for f(x): when a = 2 and Ax = 2+x %3D (Use decimal…

A:

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1

A: Given that

Q: Find the slpoe of the secant line between the values x 1 =-1 and x 2 =3 for f(x) = 8x - 3

A: Givenf(x)=8x-3x1=-1  x2=3

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: Verify the Mean Value Theorem for f(x) = In(6x + 1) on | 0, %3D

A:

Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

A:

Q: Approximate the zero of f(x) = x' - x + 3 in [-2, -1] to within 0.00001. Show your work!!!

A:

Q: 4. Assume that æ € [0, 1] and write the error in the approximation to the error function using the…

A: