Open Middle®
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.