`f(x) = x^4 - 32x + 4` Find the critical numbers, open intervals on which the function is increasing or decreasing, apply first derivative test to identify all relative extrema.
- print Print
- list Cite
Expert Answers
mathace
| Certified Educator
calendarEducator since 2015
write489 answers
starTop subject is Math
Given: `f(x)=x^4-32x+4`
Find the critical numbers by setting the first derivative equal to zero and solving for the x value(s).
`f'(x)=4x^3-32=0`
`4x^3=32`
`x^3=8`
`x=2`
The critical value is x=2.
If f'(x)>0 the function is...
(The entire section contains 124 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- `f(x) = sin(x) + cos(x)` Consider the function on the interval (0, 2pi). Find the open...
- 2 Educator Answers
- `f(x) = x + 2sin(x)` Consider the function on the interval (0, 2pi). Find the open...
- 1 Educator Answer
- `f(x) = x/2 + cos(x)` Consider the function on the interval (0, 2pi). Find the open...
- 1 Educator Answer
- `f(x) = sin(x) cos(x) + 5` Consider the function on the interval (0, 2pi). Find the open...
- 1 Educator Answer
- `f(x) = x/(x - 5)` Find the critical numbers, open intervals on which the function is...
- 1 Educator Answer