8. What are all the roots of the function f(x) = (x2 + 1)(x- 2)?

Q: d the second derivative of the functi =) = [3x° +6}* a. f" = 90x*(6+3x)ʻ(24+90x°) b. f" = 90x*(6…

A: We have to choose the correct answer from the given options according to the given information

Q: -1 if f(x) = xtan ,"x,find f' (/3 )by first principle

A:

Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

Q: 2.2 Use the Cauchy-Riemann equation to determine if the function f(2) =r- i(2-y)" is analytic or…

A:

Q: Find the first and second derivatives of the functio f(x) = x(x² + 4)2 %3D f'(x) = %3D f" (x) = %3D

A:

Q: Show that u = 3x^2y + 2x^2 - y^3- 2y^2 is a harmonic function.

A: Given: u=3x2y+2x2-y3-2y2 To show: u is a harmonic function.

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 Intermediate Value Theorem to show that there is a root of the given equation in the…

A: By intermediate value theorem, if fx is continuous on an interval  a,b and fa≠fb, then there exist a…

Q: 14. What is the first derivative of f (x) = (x²- 4)(3x - 2)? %3D a. 9x2- 4x – 12 С. 6х d. (x + 2)(x…

A: first derivative of f(x) = (x2 -4)(3x-2) f(x) = 3x3 -2x2-12x +8 now df(x)/dx = 9x2 -4x -12 so answer…

Q: 5. Use the definition of derivatives to find f'(2) given that f(x) = 2x² -r+1

A: According to our company guidelines we are supposed to answer only one question since you have asked…

Q: Find the roots of the function f(x)=(2x-1)(x2+2x-3) with x belong to R

A: f(x)=(2x-1)(x2+2x-3)=0 We have find all the real numbers that make f(x)=0 because it is given that x…

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: Q3 : Use Fixed Point method to find the root of the following function: f(x) = 4x – x + tan-(x)

A: Given function is fx:4x-x3+tan-1x=0. Substitute different values of x to get the interval in which…

Q: Example 2: Using the False Position method, find an approximated root of the function: f(x) = x² –…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

Q: 7. Consider the function *+1 if r< 2 f(x) = 3-1 if z 2 2 (a) Show that ƒ has no fixed point.

A:

Q: Use the Second Derivative Test to find the Maximum and Minimum value(s) of the function 3 f(x) x* -…

A: We have the given function as fx=32x2-4x+lnx For maxima/minima, we need to calculate f'x as…

Q: 5. Use the Intermediate Value Theorem to show that the function f(x) = x³ + x² – 1 has a zero…

A:

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: Find the derivative 2x %3D 1-x2 (1–x2)? 2 1-x2 (1-x2)? O None of these

A: We use Quotient rule to solve this derivative

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

A: To show the f(x) has roots between a and b we have to show that

Q: 2. Use the first and second derivatives to obtain sketches of the function below. 4x+2 f(x) = %3D…

A:

Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

A:

Q: (2022) , find feua (0) (1-x3 2x given f(x) 2

A:

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

A: Given that: f(x)=x2+2x-3x-1

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: 3- Find the root of function F(x) = x² – 10 Using XL=3 , X,-4 , ɛ = 0.1

A: given function Fx=x2-10 with condition XL=3, Xu=4, εS=0.1 claim- find the roots of the function

Q: (b) Find the derivative of f (x) = (x² + 2) (8x − 5) by using the product rule. Let g (x) = x² + 2…

A:

Q: 6. Obtain the TSE of f(x)=2x-² in powers of (x-1).

A: Solution is here

Q: What is the domain of g(x)=ln(25x-x^2) Show all the work.

A:

Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

A:

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

A:

Q: A goldsmith finds that the demand for gold is governed by p(x) = –x² + nx, where z is in (troy)…

A:

Q: -4 - Find the derivative for the function f(x) = (5x−4+ 3x + 7) (8x−³ − 7x + 10) 5. Do not simplify…

A: Given, f(x)=5x-4+3x+78x-3-7x+105

Q: 1) Find the derivative of f(x)= 2x³+ 2x +12. Then evaluate the

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

Q: Find a point 2o where the function f (2) = (z – 12 – 12i) (z – 12 – 12i)differentiable. What is the…

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: The derivative of f(x) = 10 (x2 + 13z) is О 10х + 130 О 10х ?(2т + 13) O 10 O -10x 3(2x + 13) O -…

A:

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

A:

Q: Let f(x)=1x−2 ; for what values of x , f(x) will be discontinuous?

A:

Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

A:

Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x&lt;2b                     if x=21x-2-cx2-2x  if x&gt;2…

Q: 2. Find the derivative of f (x) = (3x – 2x? )(5 + 4x) using the product rule

A:

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

A:

Q: 3 1. 15. f(x) = 4 *+ %3D 4

A: Given,f(x)=14x+34

Q: point =)=at x = 2 -5 at x = -2 x² +1

A: Solving

Q: What is the derivative of f(x) = -3? Do not include "f'(æ) =" in your answer. For example, if you…

A: Given            f(x)=-3

Q: The line tangent to the graph of g(x) = x³ – 4x +1 at the point (2, 1) is given by the formula L(x)…

A:

Q: 7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

A:

Q: Q3\ Find the second derivative of the funetion F(x)= 3x + 2x - 6x2 -4

A: