Thanks for looking at my question!! I really appreciate it.
Given the following data for a function f:
x: 1.1 1.3 1.5 1.7 1.9 2.1
f'(x): 12 15 21 23 24 25
Estimate f ' (1.7).
The answer should be around 7.5, I just don't know how to get there.
Write an equation for the tangent line to the graph of f at x= 1.7
Given the following data for a function f:
x: 1.1 1.3 1.5 1.7 1.9 2.1
f'(x): 12 15 21 23 24 25
Estimate f ' (1.7).
The answer should be around 7.5, I just don't know how to get there.
Write an equation for the tangent line to the graph of f at x= 1.7
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to find the derivative of 1.7 we will try to find the slope of teh secant line. So pick the points.
(1.5,21) and (1.9,24).
find the slope of th line by using (y2-y1)/(x2-x1)
the numbers are subscripts.
(24-21)/(1.9-1.5)=3/(0.4)=7.5.
so the f'(1.7) is 7.5
if we wanted to find f'(1.3) we will use the point that comes right before (1.3,15) and right after (1.3,15).
the points we will use to find f'(1.3) will be (1.1,12) and (1.5,21).
Remember the closer the two points of the secant line is the closer we get to find the tangent line.
(1.5,21) and (1.9,24).
find the slope of th line by using (y2-y1)/(x2-x1)
the numbers are subscripts.
(24-21)/(1.9-1.5)=3/(0.4)=7.5.
so the f'(1.7) is 7.5
if we wanted to find f'(1.3) we will use the point that comes right before (1.3,15) and right after (1.3,15).
the points we will use to find f'(1.3) will be (1.1,12) and (1.5,21).
Remember the closer the two points of the secant line is the closer we get to find the tangent line.
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Nope. If Im reading this correctly, your second row of numbers are already derivatives evaluated at points. According to your chart, f'(1.7)=23
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f'(1.7)=(1.9-1.5) / (24-21)= 7.5.