Directions: Using the digits 1-6, at most one time each, create an exponential function of base e whose derivative at x = 3 is 2.

### Hint

What is the process for finding the derivative?

What will make e^x ‘disappear’?

What will make e^x ‘disappear’?

### Answer

y=e^(2x-6)

Source: Christine Relleva

Hi Christine! I think you need a factor of 2 outside the exponential function like 2e^(x-3). As a follow-up you might ask students to check g'(3) if

g(x)= (2/e^3)•e^x. Then ask, “Are the solutions equivalent?”. Keep writing these great problems!😊

Dave

I think Christine’s original problem and solution work. The function doesn’t need the factor 2 since you get that when you do the derivative.