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

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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.