GSP? Like Geometer's Sketchpad?
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
Your incorrect f(x):
f (x) = 〖2x〗 ^ 6 + 〖3x〗 〖3x ^ 5 + ^ 3〗 - 〖2x〗 ^ 2. [=Incorrect]
Your correct f(x):
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:
f'(x)=0 root:
f''(x) = 0 roots: