Two hundred eight thousand five hundred sixty one in standard form

Find the absolute maximum and minimum values of the function below. f(x) = x3 − 9x2 + 3, − 3 2 ≤ x ≤ 12 Solution Since f is cont

Neko [114]

Answer:

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

Step-by-step explanation:

The correct statement is described below:

Find the absolute maximum and minimum values of the function below:

$f(x) = x^{3}-9\cdot x^{2}+ 3$ , $2 \leq x \leq 12$

Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.

First, we obtain the first derivative of the function and equalize it to zero:

$f'(x) = 3\cdot x^{2}-18\cdot x$

$3\cdot x^{2}-18\cdot x = 0$

$3\cdot x \cdot (x-6) = 0$ (Eq. 1)

As we can see, only a solution is a valid critical value. That is: $x = 6$

Second, we determine the second derivative formula and evaluate it at the only critical point:

$f''(x) = 6\cdot x -18$ (Eq. 2)

x = 6

$f''(6) = 6\cdot (6)-18$

$f''(6) =18$ (Absolute minimum)

Third, we evaluate the function at each extreme of the given interval and the critical point as well:

x = 2

$f(2) = 2^{3}-9\cdot (2)^{2}+3$

$f(2) = -25$

x = 6

$f(6) = 6^{3}-9\cdot (6)^{2}+3$

$f(6) = -105$

x = 12

$f(12) = 12^{3}-9\cdot (12)^{2}+3$

$f(12) = 435$

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

6 0

3 years ago

Find y using Pythagorean theorem or proportion

Tcecarenko [31]

We have three similar triangles, let's see if we can get this right, right vertex first, then other vertex from small side:

EDF ~ GDE ~ GEF

As ratios that means

ED:DF:EF = GD:DE:GE = GE:EF:GF

x:20:y = 5:x:GE = GE:y:15

Since we're after y we choose

20/y = y/15

20(15) = y²

y² = 300

y = 10√3

y ≈ 17.32

4 0

3 years ago

How much does 8% go into $14.00 please explain your work how you got that answer

abruzzese [7]

Answer:

175

Step-by-step explanation:

give brainlist

7 0

3 years ago

The length of triangle base is 26. A line, which is parallel to the base divides the triangle into two equal area parts. Find th

Yanka [14]

Answer:

Step-by-step explanation:

It is given that the length of triangle base is 26, then let ABC be the triangle and BC be the base of the triangle=26.Let DE be the parallel line to the base that divides triangle ABC into two equal area parts.

Now, Let AD=a, DB=b, DE=c, AE=d and EC=e, then

Since, triangle ABC is similar to triangle ADE, thus using basic proportions, we get

$\frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}$

$\frac{AD}{AD+DB}=\frac{DE}{BC}=\frac{AE}{AE+EC}$

$\frac{a}{a+b}=\frac{c}{26}=\frac{d}{d+e}$

Taking the first two equalities,we get

$\frac{a}{a+b}=\frac{c}{26}$

$c=\frac{26a}{a+b}$

Thus, the length of the segment between triangle legs is $\frac{26a}{a+b}$

7 0

4 years ago

Solve for T<br><br>10t = -50

Gemiola [76]

Answer: t=-5

Step-by-step explanation:

if 10t=-50, you have to solve for the equation. to solve, you have to get the variable by itself. to get the variable by itself, you have to divide both sides by 10. 10t/10=-50/10. t=-5

7 0

3 years ago

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