Mathematics, 07.07.2019 00:30 nicoleh2015

The absolute minimum value of x4 – x2 – 2x+ 5 (a) is equal to 5 (b) is equal to 3 (c) is equal to 7 (d) does not exist

Answers: 1

Show answers

Answers

Answer from: 2005AngelMoore

Answer-

The abs. minimum value of the given function was found to be 3.

Solution-

Here, the given function is,

f(x)=x^4-x^2-2x+5

Then, calculating its first derivative,

${f}'(x)=4x^3-2x-2$

Then, calculating its second derivative,

${f}''(x)=12x^2-2$

Then, calculating all the critical values of the given function by equating the first derivative to 0,

$\Rightarrow {f}'(x)=0$

$\Rightarrow 4x^3-2x-2=0$

$\Rightarrow 2x^3-x-1=0$

$\Rightarrow 2x^3-2x+x-1=0$

$\Rightarrow 2x(x^2-1)+(x-1)=0$

$\Rightarrow 2x(x+1)(x-1)+(x-1)=0$

$\Rightarrow (x-1)(2x(x+1)+1)=0$

$\Rightarrow (x-1)(2x^2+2x+1)=0$

$\Rightarrow (x-1)=0$ ( ∵ ignoring the imaginary roots)

$\Rightarrow x=1$

Putting the value of x, in the second derivative,

${f}''(1)=12(1)^2-2=10$

As, the value of f"(x) is positive, the function attains its minimum value at x=1.

So, f(1) will give the absolute minimum value of the function,

f(1)=(1)^4-(1)^2-2(1)+5=3

∴ The abs. minimum value of the given function is 3.

Answer from: Quest

definitely a. the others have almost all data points on one side of the line.

step-by-step explanation:

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 19:00, naomicervero

Four individuals pool money together to start a new business and agree to split the profits equally. n invests $6,000, x invests $2,000, y invests $8,000 and z invests $4,000. if the profits for the first month were $100,000, y receives than if the profits were divided in proportion to how much they invested.

Answers: 3

continue

Mathematics, 21.06.2019 19:00, towlesam

X+ y = 5 ; x - y =3 solve using linear combination

Answers: 2

continue

Mathematics, 21.06.2019 19:20, kkmoney

Will give brainliest immeadeately true or false: the origin woud be included in the solution set for the inequality: y< 2x-5

Answers: 1

continue

Mathematics, 21.06.2019 19:20, Kimb9820

Which letters from the table represent like terms? a and b b and c a and d b and d