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kaylacornish06
22.03.2021 •
Mathematics
HELP ASAP PLEASE PLEASE
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Ответ:
Try line 2. It lines up with the most points
Ответ:
f(6) = 3
f'(6) = 1/6
Step-by-step explanation:
Remember that for a function f(x), we define f'(x) as the slope of the tangent line to the point (x, f(x))
We know that:
y = f(x) passes through the point (6, 3)
Then we already know that:
f(6) = 3.
Now we also know that the tangent at this point, also passes through (0, 2)
Remember that a line can be written as:
y = a*x + b
Where in this case, a = f'(6)
so we just want to find the slope of this line.
Remember that for a line that passes through (x₁, y₁) and (x₂, y₂) the slope is given by:
a = (y₂ - y₁)/(x₂ - x₁)
And we know that the tangent line passes through the points (0, 2) and (6, 3)
Then the slope is:
a = (3 - 2)/(6 - 0) = 1/6
Then we have:
a = f'(6) =1/6