. Use the figures below to find the indicated derivatives.
Doug C. answered • 02/23/22
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Here are some hints:
h(x) = f(x)g(x), so by the product rule:
h'(x) = f(x)g'(x) + g(x)f'(x)
To find h'(0) determine:
f(0)
g(0)
f'(0)
g'(0).
Remember that f'(0) (for example) is the slope of the tangent line to the function at the point where the x-coordinate equals 0, which looks to be the slope between (0, -1/2) and (1,0) = 1/2. See if you can take if from there.
Doug C.
If I was finding g'(0) based on the graph, I would find the slope between (-3/2,-2) and (3/2,2). And just like you did for f'(0), use (-1/2,-1) and (1,0)--better than what I originally suggested. And f(0)=-2/3? g(0)=0. So, h'(0) = (-2/3)(4/3)+0(2/3) = ? Looks like the answer should be negative.
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02/23/22
Mariam A.
Thank you so much for your help!!
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02/23/22
Mariam A.
So will it be to get the slope of two points (1,0) and (2,2/3), so I got the slope 2/3 for f'(0) and the last answer will be 8/9?02/23/22