How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given #y=x^5-2x^4-3x^3+5x^2+4x-1#?
1 Answer
Graphical method reveals x-intercepts ( y = 0 ) :
Explanation:
As the sum of the coefficients in
The first graph indicates end behavior of
The second gives first approximations to the three x-intercept, of
which -1 is exact.
The next improves the positive intercept to 0.205.
The other negative intercept is improved to -1.15, using root-
bracketing method.
The last is for f', giving four turning points as zeros of f'.
graph{x^5-2x^4-3x^3+5x^2+4x-1 [-12.49, 12.49, -6.21, 6.28]}
graph{x^5-2x^4-3x^3+5x^2+4x-1 [-2.5, 2.5, -1.25, 1.25]}
graph{x^5-2x^4-3x^3+5x^2+4x-1 [.204 .206, -1.25, 1.25]}
graph{5x^4-8x^3-9x^2+10x+4 [-2.122, 2.121, -1.06, 1.062]}
