DIFFERENTIATION

Question

The diagram shows the curve y = (3 − x)e^−2x and its minimum point M. The curve intersects the x-axis at A and the y-axis at B. (i) Calculate the x-coordinate of M

Answer 1

The intersections at A and B have no relevance to M.

 

Take the derivative of y and set it equal to zero.  Then solve for x.  This where the minimum occurs.

 

y' = 0

 

-xe^-2x - 2(3 - x)e^-2x = 0

 

e^-2x(-x - 2(3 - x)) = 0

 

e^2x(-6 + x) = 0

 

x = 6

 

The x-coordinate of point M is x=6.