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1 year ago

The graph of the function f(x) = (x − 3)(x + 1) is shown.

1 answer:

3 0

The expression that describes all of the values for which the graph is positive and decreasing is all real values of x where x < -1

<h3>Which describes all of the values for which the graph is positive and decreasing?</h3>

The equation of the function is given as:

f(x) = (x - 3)(x + 1)

When the value of the graph is positive, we have:

f(x) > 0

So, the function becomes

(x - 3)(x + 1) > 0

Split the above inequality

x - 3 > 0 and x + 1 > 0

Solve for x in the inequalities

x > 3 and x > -1

Hence, the expression that describes all of the values for which the graph is positive and decreasing is all real values of x where x < -1

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Consider the function f ( x ) = − 2 x 3 + 27 x 2 − 108 x + 9 . For this function there are three important open intervals: ( − [

Darya [45]

Answer:

A=3 and B=6

Step-by-step explanation:

Increasing and Decreasing Intervals of Functions

Given f(x) as a real function and f'(x) its first derivative.

If f'(a)>0 the function is increasing in x=a

If f'(a)<0 the function is decreasing in x=a

If f'(a)=0 the function has a critical point in x=a

As we can see, the critical points may define open intervals where the function has different behaviors.

We have

$f ( x ) = - 2 x^3 + 27 x^2 - 108 x + 9$

Computing the first derivative:

$f' ( x ) = - 6 x^3 + 54 x - 108$

We find the critical points equating f'(x) to zero

$- 6 x^3 + 54 x - 108=0$

Simplifying by -6

$x^2 -9 x +18=0$

We get the critical points

$x=3,\ x=6$

They define the following intervals

$(-\infty,3),\ (3,6),\ (6,+\infty)$

Thus A=3 and B=6

3 0

3 years ago

M divided by 6 = 21 so what does m equal

loris [4]

Answer:

Step-by-step explanation:

M equals 3.5

6 0

3 years ago

Consider the function f(x) = 20/√x and its second-degree polynomial P2 (x) = 20 - 10(x-1) + 7.5(x-1)^2 at x=0.8. Compute the val

krok68 [10]

Answer:

$f (0.8) = 22.3607$ and $P_{2} (0.8) = 22.300$ .

Step-by-step explanation:

According to the statement, $f (x) = \frac{20}{\sqrt{x}}$ and $P_{2}(x) = 20 - 10 (x-1) + 7.5 (x-1) ^ 2$ . Based on these definitions, at $x=0.8$ produce: