6 pc Let f(x) = x3 + x+4 and g(x) = 2x + 3 in z,[x]. Then, upon dividing f(x) by g(x), we get O The quotient is 1+3x + 3x 2 and the remainder is 1 O None of these O The quotient is 4+2x+2x^2 and the remainder is 1 O The quotient is 6 +x+ 4x^2 and the remainder is 0

Q: Find all the rational zeros of the function f(x) = 2x - 9x4 + 9x³ - 3x² + 7x + 6. -1, 2 x = 을 3,2 x…

A: Roots satisfyf(x)=0f(x)=2x5-9x4+9x3-3x2+7x+6f(-1)=-24f(1)=12Options, A and E ruled…

Q: 1. Express the polynomial f(x) = 4x3 – 5x2 + 2x – 3 as a power of x + 2.

A:

Q: Let f(x) = x³-212-9. If f(3) = 0, then (x-3) is a factor of f(x). O True O False

A: factor theorem states that if f(x) be a polynomial of degree n , and (x-a) is a factor of f(x) then…

Q: f (x) = x - 3x +1 and g(x 4x2 + x +5. Which one of the Let following expressions is equivalent to…

A: To find f(x)+g(x).

Q: Find the remainder when f(x) = x7 + 3x5 + x - 1 is divided by x2 +1 in Z5[x].

A:

Q: 1. The function f(z) factors to f() = (* + 2)(ar + bz + c). Find (a + 6+ c). S(z) = 3+3r-5x+2 (a) 5…

A:

Q: Let f(x) = 2x2 - 1 and g(x)= 1 + x². Find (f o f)(x). O x* +2x² +2 4 O 4x4 – 4x2 + 2 | 4 O 2x* + 4x²…

A:

Q: 2 v2x-x2 XY xydydx 0 0

A:

Q: = x? – 5x + 7 has roots a and B. Use symmetric Suppose that f(x) functions to find a + B, aß, a² +…

A: If we have a quadratic equation ax2+bx+c=0 and α and β are the roots then: α+β=-ba αβ=ca We can use…

Q: exp(x) = ex ?  Is it just a matter of notation, or does exp( ) mean something else?

A: Yes this is true exp(x) = e^x  exp(x) is command in coding language to type e^x

Q: fx) = x-x, g(x) = 9-2r, and h(x) = x² + 2x-63

A: Given f(x) = x2-x, h(x) = x2+2x-63 To find the function (f-h)(x) By definition of the difference of…

Q: For P(x)=6x* –18x² +6x² – 30x +36 -

A: given that P(x)=6x4-18x3+6x2-30x+36

Q: Given f(x)= x^3 − 6x^2+9x, find the multiplicity of the zero at x = 3

A:

Q: Let f(x)= = -2 x²+3x O Only 0 O Only 3 O Only -3 Only 0 and 3 What values of x have to be excluded…

A: given  f(x)=-2x2+3xfor domain  x2+3x≠0

Q: the function f(x) = k(x - s)(x - t)(x - u)^2 has: * O 3 zeros O 4 zeros O no turning points O 4…

A: Zeros of a function are those points where function has value zero. Hence f(x)=0 implies…

Q: Calculate R5 for f(x)=4x2+6x over [-1,1]

A: The objective of this question is to calculate the Riemann sum, specifically R5, for the function…

Q: Verify that x² +1 = (x² + v2x + 1)(x² – V2x + 1). %3D

A: **Since you have asked to solve question no. 42, you will solve that question.Question 42.We need to…

Q: 8. Find one zero of the polynomial f(x)=2x-x-6x+3 %3D

A: Given function is: Apply rational root theorem to get roots of polynomial. If the polynomial has a…

Q: Determine Q(x) when P(x)=x³-5x2-3x+2 is divided by x-1 and then expressed in the form Select one: O…

A:

Q: y = (2x+5) (x-4) y = (4x³- 5x)³ 11. y = 10. ƒ(x) = 2x-1 x+6

A:

Q: B Sin3X 6653X + X3

A:

Q: Find f(x + Ax) by substituting x + Ax in place of x in f(x) = 9x² - 5x. f(x + Ax) = 9( x+ Ax D² - 5(…

A: To find the f(x+∆x)

Q: A variable circle passes through the point A(a, b) and touches the x-axis. Show that the locus o the…

A:

Q: Find In such that: F(x) = x²³-8x²+ 9x +18=0

A: The given polynomial fuction is

Q: f(x) =-2x - 4 if xs2 |4x -9 if x> 2 3.

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.