I think the topic sums it up pretty well. I have no idea what I'm supposed to be doing here.
Maybe I figured it out now.
u'(1) = f(1) g'(1) + g(1) f'(1)
They are piecewise functions.
So u(x) and v(x) will be piecewise functions aswell.
The intervals are (-∞,0), (0,2) and (2,∞)
(I assumed they don't change after the graph ends)
That's not the question though, they want me to differentiate a combination of the two.
I would do it in the following steps:
1) Find the functions f(x) and g(x), they're piecewise and linear.
2) Find the functions u(x) and v(x), they're also piece wise.
3) Derivate the functions.
4) Evaluate the u'(x) in 1 and v(x) in 5.
The beginning is good, but why zero in the end?
What is the geometric meaning of the derivative?
That is correct. What are the values of f(1), f'(1), g(1) and g'(1)?
The meaning is instantaneous rate of change.
Lets see here
(2)(-1)+(1)(2) = 0
Still get it to zero.
f(1) = 2
g'(1) = -1
g(1) = 1
f'(1) = 2
For x between 0 and 2, the graph of f is the straight line between (0, 0) and (2, 4): f(x)= 2x. For x between 0 and 2, the graph of y is the straight line between (0, 2) and (2, 0): g(x)= 2- x. Their product is fg(x)= 2x(2- x)= 4x- 2x^2. (fg)'= 4- 2x and at x= 1, that is, indeed, 0.
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