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For the function below, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing
toxx ?
f(x)= 3%
X-X-112x - 4
(a) The critical number(s) is/are -
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
(b) on which intervals is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. Increasing on
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
OB. Never increasing
(c) On which intervals is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
ОО
A. Never decreasing
B. Decreasing on
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression, Vse a comma to senartowo

For the function below find a the critical numbers b the open intervals where the function is increasing and c the open intervals where it is decreasing toxx fx class=

Respuesta :

Step-by-step explanation:

We must do the first derivative test. Here is the steps:

Step 1: Differentiate the polynomial once

we get

[tex]2 {x}^{2} - 2x - 112[/tex]

Step 2: Set this equal to zero and solve for x.

[tex]2 {x}^{2} - 2x - 112 = 0[/tex]

[tex] {x}^{2} - x - 56 = 0[/tex]

[tex](x - 8)(x + 7) = 0[/tex]

[tex]x = 8[/tex]

[tex]x = - 7[/tex]

The solutions are your critical points.

So our critical points are (8,-7).

Step 3: Plot -7 and 8 on a number line. First, pick a number lesser than -7 and plug plug in the derivative function.

Let use -10.

[tex]( - 10 - 8)( - 10 + 7) = 54[/tex]

Since that number is positive, this means are increasing when (-oo,-7)

Next, pick a number greater than 8. Let use 9.

[tex](9 - 8)(9 + 7) = 16[/tex]

Since that is positive, the interval is increasing whe (8,oo)

C. If we pick a number in between -7 and 8, we will get a negative number which means the function is decreasing on interval (-7,8)

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