(4) Let f(x) = xª + 2x³ + 6x² + x – 1. Find, with proof, the number of zeroes of f.

Q: Use the Intermediate Value Theorem to approximate the real zero of f(x) = x3 − x2 + 1.

A: Here given function as fx=x3-x2+1 Now  f-1=-12--12+1=-1-1+1=-1<0 and f0=02-02+1=0-0+1=1>0

Q: Compute f"(a) algebraically for a = 3. f(x) = 7x²+x

A:

Q: Determine the real root of f(x)= -25+82x-90x2+44x3-8x4+0.7x5. Iterate until the estimated error…

A: The False-Position (also known as Regula-Falsi) method uses the formula:…

Q: Find the domain of f(x) = Vx + 3 + Vx - 1.

A: Given that the function f(x) = x+3 +x-1 To find the domain of f(x).

Q: Show that f(x)=x5-x3-1 has a zero between 1 and 2.

A:

Q: 2. Find the zeros of f(x)=x² -x-12.

A:

Q: Let f(x)=8x^3-18x^2-11x+15. Solve, algebraically, f(x)=0

A:

Q: Show that f(x)= x3 + 3x + 1 has exactly one real root

A: fx=x3+3x+1i fx is continuous on -1,0ii f-1=-13+3-1+1           =-3<0  f0=1>0Therefore by…

Q: Given that f(x) = x² – 6x + 8 and = x – 2, find f(x)+ g(x) and - - express the result in standard…

A:

Q: 15. Determine the zeros for and the end behavior of f(x) = x(x – 4)(x +2)*.

A: Given function is  F(x) = x(x-4)(x+2)^2

Q: Determine the real root of f(x)= -25+82x-90x2+44x3-8x4+0.7x5. Iterate until the estimated error…

A: given: fx = -25+82x-90x2+44x3-8x4+0.7x5To find root we put fx =0. ⇒-25+82x-90x2+44x3-8x4+0.7x5 = 0…

Q: Find the potential rational zero of f(x)=5x^(4)+2x^(2)-6x-5.

A:

Q: 4. Find the zeros of f(x) = x² + x – 3.

A: We know that, for a quadratic function fx=ax2+bx+c, the zeros of of fx is given as x=-b±b2-4ac2a…

Q: Given that f(x) = x2 - 8x + 15  and g(x) = x - 5     find (f ÷ g)(x) and express the result in…

A: Given  f(x) =x2-8x+15           g(x) =x-5We find (f÷g)(x)

Q: 5. Find the asymptotic behavior of the polynomial f(x) = -x"+4æ® + 2x³ – x³ + 10x? – 12x – 10 (i.e.…

A:

Q: 4. Find the absolute maxima and minima for f(x) = 4x - 9x2- 12x-1 on the closed interval [0, 4].

A:

Q: Find an nth-degree polynomial function with real coefficients satisfying the given conditions as : n…

A: Since 1 and i are the zeroes of the polynomial, therefore

Q: 5. Find all zeros for f (x) =x°+x³+2x2– 12x+8

A: Solution

Q: Find the f'(x) of f(x) = -2x³ + x⁴ + 2 over 3

A: Given:  f(x)=−2x3+x4+23 To Find: f'(x)=?

Q: 1 Find the domain of the function f(x) V4 - 2x – x²

A: fx=14-2x-x2

Q: Given that f(x)=x^2+3x-70 and g(x)=x-7, find (f-g)(x) and express the result in standard form

A:

Q: 7. Find the natural domain of the function f(x) = V4– 3x .

A:

Q: 1. How many non-real zeros does the function f(x) = x - 2x + 8x-16x have? 1. 0 2. 2 3. 3 4. 4

A:

Q: Consider f (x) =x³ – 6x²+9x +3 defined on the closed interval .At which value of x does the absolute…

A:

Q: Find a polynomial function f(x) with integer coefficients and leading coefficient 1, such that f(x)…

A: We have to find function

Q: Let  ƒ(x) = 6x2 − 2 and g(x) = x2 − 2x + 5 to find the value. ƒ(t + 1)

A: Given: fx=6x2-2gx=x2-2x+5 The objective is to find the value of ft+1

Q: Find the value of x in f(x) = x^2-6x+8

A: Given ,  f(x) = x2 - 6x + 8 We have to find the value of x  x2 - 6x + 8 = 0  x2 - 4x - 2x + 8 = 0

Q: In Problem,explain why the facts given are contradictory.

A: Zero of a function is a point in its domain for which the function takes the value equal to 0. A…

Q: 2) Find all points of inflection in the function f (x) = x 3 + 3x2 – 24x + 12.

A:

Q: Find a polynomial f (x) that satisfies the equationxf"(x) + f (x) = x2.

A: Quadratic equation are those equation in which highest power of the equation is 2 and it has two…

Q: 1. Find the domain of f(x) = v2 + 5.x – 3x².

A: The domain of a function is the set of input or argument values for which the function is real and…

Q: 7. Find the domain of f(x) = V² + 2x – 3 and write it in interval notation.

A: The solution is given below.

Q: Find the domain of the function  f(x)= In(x^2+5x+6)

A:

Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ |

A: find the polynomial f(x) for which  x fx-1=x-3 fx ∀x for x=0 x fx-1=x-3 fx ∀x

Q: 1. Express the quadratic function f1x2  x2  x  6 in standard form, and sketch its graph.

A: Given: f(x)=x2−x−6

Q: Consider f(x) =x³- 6x² + 9x + 3 defined on the closed interval 13 At which value of x does the…

A:

Q: (a) By sketching the graph of the function f(x) = x³ + x² – 1, show that the equation f (x) = 0 has…

A: The root of the equation is 0.755 Also it is evident that it is lying between 0 and 1

Q: Find a third-degree polynomial function f(x) with real coefficients that has -3 and i as zeros and…

A: Polynomial: The polynomial which has real co-efficient and of third degree. f(x) has three zeros…

Q: Find the formula of f(x) a polynomial function of a least degree

A: At x=-4 the curve cuts the x-axis. So x=-4 has multiplicity=1 So the factor is (x-(-4))=(x+4)   At…

Q: intermediate value theorem

A:

Q: Find f such that f'(x)= 7x +7x-2 and f(0)= 8.

A:

Q: Find the zeros of f (x) = x^(4)-4x^(3)-12x^(2) pre caluclus

A: Given : f(x)=x4-4x3-12x2 To find : We have to determine the zeros of f(x).

Q: the domain for the real valued function f(x) = is 2x-4 2x+1

A: Given : fx = 2x+12x-4

Q: Find f such that f′(x)=7x2+9x−2 and f(0)=7.

A: We integrate the given function and use the given condition f(0)= 7 .

Q: Suppose f(x) has a zero at an x-value of 3. What would a zero of g(x) be if g(x) = -2f(3x + 1)? %3D

A: Given that f(x) has a zero at x = 3, it means f(3) = 0To find the zero of g(x), where g(x) = -2f(3x…

Q: Find f such that f'(x) = 8x² + 3x – 7 and f(0) = 2. f(x) =O

A:

Q: 12. Find all the rational zeros for the function. f(x) = 5x³ – 16x² – 47x + 10 - -10 -2 1/2

A:

Q: Find the absolute extrema of f(x) = 2x³ – 21x² + 72x on the closed interval [0, 5].

A:

Q: Find the asympototes of f(x)= x4-2/x3+1

A: f(x)= x4-2/x3+1 We can find the vertical asymptotes by finding the values that make the function…

Q: The zeros of the function f(x)=x'-9x are 1) 9, only 2) 0 and 9 3) 0 and 3, only 4) -3, 0, and 3

A: