SOLUTION: sketch the graph of the polynomial function f(x)=2x^3-x^2-8x+4. label the zeroes and maximum/mini points. show your work

Algebra ->  Trigonometry-basics -> SOLUTION: sketch the graph of the polynomial function f(x)=2x^3-x^2-8x+4. label the zeroes and maximum/mini points. show your work      Log On


   

Question 1137124: sketch the graph of the polynomial function f(x)=2x^3-x^2-8x+4. label the zeroes and maximum/mini points. show your work
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Sketch the graph of the function
f%28x%29=2x%5E3-x%5E2-8x%2B4
Solution:
1. Find the relative max and min
f′=6x%5E2-2x-8=2%283x%5E2-x-4%29=2%28x+%2B+1%29+%283x+-+4%29
critical numbers:
x=-1
x=4%2F3

f′′=12x-2

evaluate at the critical numbers
f′′%28-1%29=-12-2=-14%3C0=> f concave down
relative max at x=+-1
f%28-1%29=2%28-1%29%5E3-%28-1%29%5E2-8%28-1%29%2B4=9

=> point (-1,+9) is a relative max

f′′%284%2F3%29=12%284%2F3%29-2=14+%3E0 f concave up
relative min at x=4%2F3
f%284%2F3%29=2%284%2F3%29%5E3-%284%2F3%29%5E2-8%284%2F3%29%2B4=-3.7
=>point:(4%2F3, -3.7) is a relative min