The absolute minimum value of the function $f\left(x\right)=9{x}^{2}-18x+3$ over the interval [0,10]

(1)6

(2)-6

(3)3

(4)4

(5)1

(1)6

(2)-6

(3)3

(4)4

(5)1

hrostentsp6
2021-12-04
Answered

The absolute minimum value of the function $f\left(x\right)=9{x}^{2}-18x+3$ over the interval [0,10]

(1)6

(2)-6

(3)3

(4)4

(5)1

(1)6

(2)-6

(3)3

(4)4

(5)1

You can still ask an expert for help

Ryan Willis

Answered 2021-12-05
Author has **15** answers

Step 1

The absolute minimum value of the function

$f\left(x\right)=9{x}^{2}-18x+3$ over the interval [0,10]

Step 2

The absolute minimum value of the function

$f\left(x\right)=9{x}^{2}-18x+3$ over the interval [0,10]

In first step we need to find first derivative of f(x) and put it equal to 0

f'(x)=18x−18

put f'(x)=0

18x-18=0

18x=18

x=1

find f"(x)

$fx)=\frac{d}{dx}(18x-18)=18$ which is positive, so function has minimum value.

Step 3

Put x=1 in f(x)

$f\left(1\right)=9{\left(1\right)}^{2}-18\left(1\right)+3$

f(1)=9-18+3

f(1)=-9+3

f(1)=-6

hence minimum absolute value of function is −6

The absolute minimum value of the function

Step 2

The absolute minimum value of the function

In first step we need to find first derivative of f(x) and put it equal to 0

f'(x)=18x−18

put f'(x)=0

18x-18=0

18x=18

x=1

find f"(x)

Step 3

Put x=1 in f(x)

f(1)=9-18+3

f(1)=-9+3

f(1)=-6

hence minimum absolute value of function is −6

asked 2020-10-18

Lesson 3−23 - 23−2

Some Attributes of Polynomial Functions

$a.f\left(x\right)=5x-x3+3x5-2f\left(x\right)=5x-{x}^{3}+3{x}^{5}-2f\left(x\right)=5x-x3+3x5-2$

$b.f\left(x\right)=-22x3-8x4-2x+7f\left(x\right)=-\frac{2}{2}{x}^{3}-8{x}^{4}-2x+7f\left(x\right)=-22x3-8x4-2x+7$

Some Attributes of Polynomial Functions

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I was reading Linear Algebra by Hoffman and Kunze and I encountered some concepts which were arguably not explained or expounded upon thoroughly. I will present my questions below, and I am looking for answers that do not invoke concepts like determinant, vector spaces etc. Note that this is an introductory chapter that assumes no knowledge of the above concepts.

Question 1: Consider a linear system A with k equations. If we form a new equation by taking a linear combination of these k equations, then any solution of A is also a solution of this new equation. Why is this so?

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Question 1: Consider a linear system A with k equations. If we form a new equation by taking a linear combination of these k equations, then any solution of A is also a solution of this new equation. Why is this so?

Question 2a: Consider two linear systems A and B. If each equation of A is a linear combination of the equations of B, then any solution of B is also a solution of A. Why is this so?

Question 2b: If each equation of A is a linear combination of the equations of B, then it is not necessary that any solution of A is also a solution of B. Why is this so?

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Solve, please:

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Solve the system

$\{\begin{array}{cc}{x}_{1}^{\prime}(t)=3{x}_{1}(t)-2{x}_{2}(t)+{e}^{2t},{x}_{1}(0)=a& \\ {x}_{2}^{\prime}(t)=4{x}_{1}(t)-3{x}_{2}(t),{x}_{2}(0)=b& \end{array}$

by using the method of diagonalization. Substitution $x=Tz$

$\{\begin{array}{cc}{x}_{1}^{\prime}(t)=3{x}_{1}(t)-2{x}_{2}(t)+{e}^{2t},{x}_{1}(0)=a& \\ {x}_{2}^{\prime}(t)=4{x}_{1}(t)-3{x}_{2}(t),{x}_{2}(0)=b& \end{array}$

by using the method of diagonalization. Substitution $x=Tz$