The equation of the tangent line of a function f at (7, 5) is y =1/7x + 4. What is f '(7)?

The derivative of a function at x=7 is the slope of the tangent line at x=7. And, since y = (1/7)x + 4 is the tangent line at at x = 7, its slope is the value of the derivative at x = 7. Therefore, f '(7) = 1/7.
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If the tangent line is y = (1/7)x + 4, the slope of the tangent line is 1/7, which is the derivative of the function at that point.

f'(x) = (1/7)x + 4

f'(7) = (1/7)(7) + 4
f'(7) = 5