Mariam A.
asked • 02/17/22Please help with the answer !!!
Let 
,. Use the figures below to find the indicated derivatives.
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1 Expert Answer
If h(x)=f*g (product, then h'(x) = f'g + g'f
At 0, g=0, so the first term is 0
At 0 g' can be obtained from the slope of the line: Using the endpoints: (2-(-2))/(1.5-(-1.5)) = 4/3
At 0 f = -2/3 (again, going by the endpoints of the line segment: the rise getting to 0 from -1 is (.5/1.5)(1) = 1/3. So 1/3 up from -1 is -2/3
Plug in.
Mariam A.
Can you please repeat again how do we get f(0) because this one I'm struggling in it.
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02/17/22
JACQUES D.
tutor
You go 1/3 of the way from -.5 to 1.0 in x. Therefore, you have to go 1/3 of the way from -1 to 0.
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02/17/22
Mariam A.
Oh, so the answer for f(0)= 2/3? and the function h'(0) will be 8/9?
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02/18/22
JACQUES D.
tutor
-2/3
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02/18/22
Mariam A.
I actually did it this way from those two points to get the slope (1,0) and (2,2/3), so I got the slope 2/3 can you state the points that you chose to get -2/3?
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02/18/22
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Gerard M.
Looks like the question got cut off, I can only see "A. h'(0) = ...". But it looks like to solve, you'll have to recall the product and quotient rules for taking derivatives, and then use the graphs to find both the value of f(x) and g(x) at x, and both f'(x) and g'(x) at x, then plug them into the product/quotient rule formulas.02/17/22