Consider the following function. f(x) = (x – 5)3 (a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Increasing: Decreasing: (b) Find the relative extrema of f. (If an answer does not exist, enter DNE.) relative maximum (х, у) %3D relative minimum (х, у) -D (c) Find the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Concave upward: Concave downward: (d) Find the inflection points, any, of f. (If an answer does not exist, enter DNE.) (x, y) =
Consider the following function. f(x) = (x – 5)3 (a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Increasing: Decreasing: (b) Find the relative extrema of f. (If an answer does not exist, enter DNE.) relative maximum (х, у) %3D relative minimum (х, у) -D (c) Find the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Concave upward: Concave downward: (d) Find the inflection points, any, of f. (If an answer does not exist, enter DNE.) (x, y) =
Consider the following function. f(x) = (x – 5)3 (a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Increasing: Decreasing: (b) Find the relative extrema of f. (If an answer does not exist, enter DNE.) relative maximum (х, у) %3D relative minimum (х, у) -D (c) Find the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Concave upward: Concave downward: (d) Find the inflection points, any, of f. (If an answer does not exist, enter DNE.) (x, y) =
Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
Increasing:
Decreasing:
(b)
Find the relative extrema of f. (If an answer does not exist, enter DNE.)
relative maximum
(x, y)
=
relative minimum
(x, y)
=
(c)
Find the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
Concave upward:
Concave downward:
(d)
Find the inflection points, if any, of f. (If an answer does not exist, enter DNE.)
(x, y) =
Transcribed Image Text:### Consider the following function.
\[ f(x) = (x - 5)^3 \]
---
#### (a) Find the intervals where the function \( f \) is increasing and where it is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
**Increasing:**
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
**Decreasing:**
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
---
#### (b) Find the relative extrema of \( f \). (If an answer does not exist, enter DNE.)
**Relative Maximum \((x, y)\) =**
\[ (\_\_\_\_\_\_\_, \_\_\_\_\_\_\_) \]
**Relative Minimum \((x, y)\) =**
\[ (\_\_\_\_\_\_\_, \_\_\_\_\_\_\_) \]
---
#### (c) Find the intervals where the graph of \( f \) is concave upward and where it is concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
**Concave upward:**
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
**Concave downward:**
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
---
#### (d) Find the inflection points, if any, of \( f \). (If an answer does not exist, enter DNE.)
**\( (x, y) \) =**
\[ (\_\_\_\_\_\_\_, \_\_\_\_\_\_\_) \]
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
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![### Consider the following function.
\[ f(x) = (x - 5)^3 \]
---
#### (a) Find the intervals where the function \( f \) is increasing and where it is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
**Increasing:**
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
**Decreasing:**
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
---
#### (b) Find the relative extrema of \( f \). (If an answer does not exist, enter DNE.)
**Relative Maximum \((x, y)\) =**
\[ (\_\_\_\_\_\_\_, \_\_\_\_\_\_\_) \]
**Relative Minimum \((x, y)\) =**
\[ (\_\_\_\_\_\_\_, \_\_\_\_\_\_\_) \]
---
#### (c) Find the intervals where the graph of \( f \) is concave upward and where it is concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
**Concave upward:**
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
**Concave downward:**
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
---
#### (d) Find the inflection points, if any, of \( f \). (If an answer does not exist, enter DNE.)
**\( (x, y) \) =**
\[ (\_\_\_\_\_\_\_, \_\_\_\_\_\_\_) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75750e15-f2b0-4135-a3c1-2da1dff37f84%2F6b11554e-681f-4ba6-bd4f-01009025a37b%2Fgcbwgc_processed.png&w=3840&q=75)
