Slope increasing

Question

If the slope of a strictly increasing function at the point (a, b) is 3, what is the slope of the inverse of the function at the point (b, a)? (2 points)

3

1

1/3

The slope cannot be determined without knowing the equation of the function.








None of these

Answer 1

Hi Gail,

 

The correct answer is 1/3. If  y = f(x), then  dy/dx  = f’(x)  Multiplying both sides by dx results in dy = f’(x)dx.  This means that y changes about f’(a) as fast as x when x = a  and x changes about 1/f’(a) times as fast as y when y = b.Therefore, the derivative of the inverse of f(x) at b is the reciprocal of the derivative f(x) when x = a.