Find the remainder when x⁵+x³+x is divided by x-3. State whether the binomial is a factor of the polynomial

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

2 years ago

10+10=? trả lời đi mà

Viktor [21]

10Answer:

10 + 10 =

Step-by-step explanation:

=20

4 0

2 years ago

What's the explicit formula for 5,10,15,20,25,30

vivado [14]

Answer:

$a_{n}$ = 5n

Step-by-step explanation:

There is a common difference d between consecutive terms

d = 10 - 5 = 15 - 10 = 20 - 15 = 25 - 20 = 30 - 25 = 5

This indicates the sequence is arithmetic with explicit formula

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 5 and d = 5 , then

$a_{n}$ = 5 + 5(n - 1) = 5 + 5n - 5 = 5n

4 0

2 years ago

Find the value of x

AURORKA [14]

Hello Alondra,

To solve this problem, you have to write a proportion using the ratios formed by the similar triangles.

Or proportion can be:
x/(x+2) = 10/15

Cross multiply to solve it:
10x + 20 = 15x
20 = 5x
4 = x

The value of x is 4.

I hope this helps,
MrEQ

6 0

3 years ago

If a central angle measures 25, then the measure of its intercepted arc is

borishaifa [10]

Medida do angulo central = medida do arco interceptado
arco = 25º e ângulo central = 25º

7 0

3 years ago