Find the values of x where the tangent line to the graph of f(x) = 1/x is parallel to the line y = −7x + 5

Answer 1

f '(x) is the slope of the tangent line of f(x). The slope of y = −7x + 5 is -7. So, being parallel, they are the same.

f '(x) = -1/x²

-1/x² = -7

1/x² = 7

x² = 1/7

x = ± √7/7