Question 1001667: What is each piece of information telling about the function exactly?
The function has these properites:
f(0) = 0
f'(1) = 0
lim x->∞ f(x) = 0
lim x->-∞ f(x) = 0
lim x->-1 f(x) = ∞
f'(x)>0 on (-∞,-1)U(1,∞)
f'(x)<0 on (-1,1)
f"(x)>0 on (-∞,-1)U(-1,3)
f"(x)<0 on (3,∞)
Please explain these have an exam and I need to know how to construct a graph from this information.
Thank you
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
| Statement | Translation |
|---|
| f(0) = 0 | The point (0,0) is on the graph of f(x) | | f'(1) = 0 | The slope of the tangent line at x = 1 is m = 0. This tangent line is horizontal | | lim x->∞ f(x) = 0 | There is a horizontal asymptote at y = 0 | | lim x->-∞ f(x) = 0 | There is a horizontal asymptote at y = 0 | | lim x->-1 f(x) = ∞ | There is a vertical asymptote at x = -1 | | f'(x)>0 on (-∞,-1)U(1,∞) | Function f(x) is increasing when x < -1 or when x > 1 | | f'(x)<0 on (-1,1) | Function f(x) is decreasing when -1 < x < 1 | | f"(x)>0 on (-∞,-1)U(-1,3) | Function f(x) is concave up when x < -1 or when -1 < x < 3 | | f"(x)<0 on (3,∞) | Function f(x) is concave down when x > 3 |
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