Question

I think there is a mistake in the Session 1recital video for graphing a derivative function. The suggested resulting function goes to +infinity from both ends, which would imply that the slope will be becoming infinitely steeper and steeper. However from the original y=f(x) function, we see that the slope is the practically the same as x goes to -infinity or +infinity. So I think the y=f'(x) should be asymptotic around some constant value. Is it correct logic?

Answer 1

You can assume that the curve is polynomial or exponential, and in these cases, the derivative will be a function of x. For example, if we had
f(x)= x^3
and f'(x)= 3x^2 and at the slope will go to infinity as x goes to infinity.

You will be hard-pressed to write down a function that wiggles around like the one in the video, but has a constant slope for large x.