Find values of x where tangent line to f(x)=(1/x) is parallel to the line y=-5x+9.

Question

I need help! I need to find the greater solution and the lesser solution of x (whatever that means).

Answer 1

The function is f ( x ) = (1 / x ).

f  ' (x ) = - 1 / x ^2.

This is the slope of the tangent line .

Compare the given line y = - 5x + 9 with slope - intercept form of a line equation is y = mx + b, where m is slope, and b is y - intercept.

Slope (m ) = - 5.

From the given data, the tangent line is parallel to y = - 5x + 9.

Parallel lines have the same slope.

So,

- 1 / x ^2 = - 5

x ^2 = 1 / 5

x = ± (1 /√5).

Therefore, greater solution of x = 1 / √5 and the lesser solution of x = - 1 /√5.