In each item, do the following analytically:



Answered question


In each item, do the following analytically: (a) find the relative extrema of f. (b) determine the values of x at which the relative extrema occur. (c) determine the intervals on which f is increasing. (d) determine the intervals on which f is decreasing. f(x)=x33x29x

Answer & Explanation



Skilled2021-08-19Added 102 answers

(a) Find the domain of the funtion f(x)=x33x29x, xR Finde the derivative f(x)=3x26x9 Find the domain of derivative f(x)=3x26x9, xR Substitute f'(x)=0 0=3x26x9 Solve equation x=1
Determine th intervals ,1,1,3
1,3,3,+ Choose the points x1=2
x4=0 Calculate the values of the derivatives f(2)=15
f(4)=15 The relative maximum at x=-1 The relative minimum is at x=3 f(x)=3x26x9, x=1
f(x)=3x26x9, x=3 Calculate the value f(1)=5
f(3)=-27 The relative maximum of the function is 5 at x=-1 The relative minimum of the function is -27 at x=3 (b) To find x-intercept, substitute f(x)=0 0=x33x29x Swap the sides x33x29x=0 Factor the expression x×(x23x9)=0 Separate onto possible cases x=0
x23x9=0 Solve the equation x=0
x=3352 There is 3 solutions (c) and (d) Let's plot the polynomial to determine the intervals of increasing and decreasing. Increase by: (,1),(3,) Decreases by: (1,3) image

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?