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I have a problem that states: Sketch the graph of a function f for which f(0)=0, f'(0)=3, f'(1)=0, and f'(2)=-1.
Please help me!
Please help me!
- Joined
- Feb 4, 2004
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- 16,582
We can't really draw pictures here. You'll need to specify the trouble you're having.
You're given a plot point, (0, 0). You're drawn that dot, right?
You're told a place where the slope is positive (so the line is increasing), where it's zero (so the line is horizontal), and where it's negative (so the line is decreasing). What have you done with that information?
Eliz.
You're given a plot point, (0, 0). You're drawn that dot, right?
You're told a place where the slope is positive (so the line is increasing), where it's zero (so the line is horizontal), and where it's negative (so the line is decreasing). What have you done with that information?
Eliz.
I believe you can start with a cubic of the form ax<sup>3</sup>+bx<sup>2</sup>+cx+d=0.
Sub in 0 for x. That'll give you d.
Take the derivative, set it equal to 3 and sub in x=0, there's c.
Do the same for the other two:
3a(1)<sup>2</sup>+2b(1)+3=0
3a(2)<sup>2</sup>+2b(2)+3=-1
Now solve for a and b.
Sub in 0 for x. That'll give you d.
Take the derivative, set it equal to 3 and sub in x=0, there's c.
Do the same for the other two:
3a(1)<sup>2</sup>+2b(1)+3=0
3a(2)<sup>2</sup>+2b(2)+3=-1
Now solve for a and b.