How do I find the x-intercepts, local maximums, and local minimums of this graph -->
f(x)=1/9(x-3)^2(x+3)^2

using a graphing calculator?

For the x-intercepts, you would set Y to 0 and solve for x.
And for max and min using a TI-83 Plus, when you're looking at your graph hit "2nd"-"Calc"(also the trace key). It is option 3 and 4 in that window for minimum and maximum.
Hope that helps.

Finding a composite fuction and iits domain

How do I find the x-intercepts, local maximums, and local minimums of this graph -->
f(x)=1/9(x-3)^2(x+3)^2
We can find x-intercepts like that:
f(x)=0 <=> 1/9(x-3)^2(x+3)^2 = 0 <=> x = 3 or x = -3
one more thing, if you want to find the local maximum/minimum => you must do like that:
f(x) = 1/9 (x-3)(x+3)(x-3)(x+3)
<=> f(x) = 1/9 (x^2 - 9 )^2
<=> f(x) = 1/9 [(x^2)^2 - 2.9.x^2 +9^2]
<=> f(x) = 1/9 (x^4 -18x^2 +81)
find f'(x)
f'(x) = 1/9(4x^3 - 36x)
find x when f'(x) = 0 <=> x = 0 or x = 3 or x = -3
then find f''(x)
f''(x) = 1/9(12x^2 - 36)
determine local maximum and minimum:
f''(0) = 1/9(12.0^2 -36) = -4 <0 => the local maximum of function at x = -4
f''(3) = 1/9(12.3^2 -36) = 8 >0
f''(-3)= 1/9[12.(-3)^2 - 36] = 8 >0
=> this function have 2 local minimum at x = -3 and x = 3
can find y when you calculate x at f(x)

f(x)=0.2x^4+0.3x^3-0.8x^2+5

Can you please start your own thread for your question. I just looked through this whole thread just to find a different thing at the end. You also haven't asked a question.

EDIT: Has been re-posted over here:
https://www.askmehelpdesk.com/math-s...in-399632.html

(That's why this is confusing.)