If the tangent line of f(x) at (6, 3) passes through the point (0, 2), what is f'(6)?
Solution:
Given that the tangent line of the curve y = f(x) passes through the two points (6, 3) and (0, 2)
In geometry,
there is a condition to find the slope of the tangent line passing through two points(x1, y1) and (x2, y2) as
m = (y2 - y1) / (x2 - x1)
If x1 = 0, y1 = 2 and x2 = 6, y2 = 3
So that the slope =
(3 - 2) / (6 - 0)
Slope (m) = 1 / 6
But the other form tangent to the curve f(x) is f'(x)
Slope of the tangent line to the curve y = f(x) is
f'(x) = m = 1/6
Therefore,
f'(6) = 1/6
If the tangent line of f(x) at (6, 3) passes through the point (0, 2), what is f'(6)?
Summary:
For a line y = mx + c slope at any point is m.If the tangent line of f(x) at (6, 3) passes through the point (0, 2) then f'(x) = m = 1/6. A tangent line is a line that touches a curve at a single point and does not cross through it.
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