If the line tangent to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f '(4)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The line tangent to y = f(x) at (4, 3) passes through the point (0, 2).

The slope of the line is (3 - 2)/(4 - 0) = 1/4

For any function f(x), the value of f'(a) is the slope of the tangent at the point x = a.

Here the slope of the tangent at x = 4 is equal to 1/4. This gives f'(4) = 1/4.

f(4) = 3 as the function passes though the point (4, 3)

The value of f'(4) = 1/4 and f(4) = 3

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