Math Help - anyone know how to solve this differentiation？

1. anyone know how to solve this differentiation？

One of this project is to design GSP project. You are given a task involving graph polynomials. f (x) = 〖2x〗 ^ 6 + 〖3x〗 〖3x ^ 5 + ^ 3〗 - 〖2x〗 ^ 2. Your graph should include the following:

Use the graph of f 'and f'' to estimate the maximum and minimum points.
Hard copy the graph to be submitted.
Calculus involved in determining the maximum and minimum points to be discussed。
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Salah satu aktiviti dalam projek ini adalah untuk merancang projek GSP. Anda diberi satu tugas melibatkan graf polynomial. f(x)=〖2x〗^6+〖3x〗^5+〖3x〗^3-〖2x〗^2. Graf anda haruslah disertakan dengan yang berikut :

Gunakan graf f’ dan f’’ untuk membuat anggaran titik maksima dan minima.
Hard copy graf hendaklah dikemukakan.
Kalkulus yang terlibat dalam menentukan titik maksima dan minima haruslah dibincangkan

3. Re: anyone know how to solve this differentiation？

To see what's going on you need to plot f, f', f'' for -.6<x<.6

f'(-.49454)=0 is a min point f(-.49454)=-4.36124

Can't yet paste the graph into message!

5. Re: anyone know how to solve this differentiation？

HOW about send to my mailbox？

6. Re: anyone know how to solve this differentiation？

f (x) = 〖2x〗 ^ 6 + 〖3x〗 〖3x ^ 5 + ^ 3〗 - 〖2x〗 ^ 2. [=Incorrect]

f(x)=〖2x〗^6+〖3x〗^5+〖3x〗^3-〖2x〗^2.

Based on the correct f(x) we have:

f(-3.8268) = 0

f'(-3.18549) = 0 => min point: f(-3.18549) = -13747.8

f'(0) = 0 => next min point f(0) = 0. double root

f'(0.0881902) = 0 => f(0.0881902) = -0.0112643

also:

f(0.128435) = 0

f(x) = blue graph
f'(x) = red graph
f''(x) = yellow graph

f(x) = 0 roots:
$\{x\to -3.8268\},\{x\to -0.0492561+0.35318 i\},\{x\to -0.0492561-0.35318 i\},\{x\to 0.\},\{x\to 0.\},\{x\to 0.128435\}$

f'(x)=0 root:
$\{\{x\to -3.18549\},\{x\to -0.0333791-0.270267 i\},\{x\to -0.0333791+0.270267 i\},\{x\to 0.\},\{x\to 0.0881902\}\}$

f''(x) = 0 roots:
$\{\{x\to -2.54453\},\{x\to -0.0165289-0.187247 i\},\{x\to -0.0165289+0.187247 i\},\{x\to 0.0463423\}\}$