### Home > APCALC > Chapter 6 > Lesson 6.1.3 > Problem 6-36

6-36.

Sketch a continuous function that satisfies all of the following conditions. Read carefully—some are limits of the *derivative*, not the function. Where is *f* non‑differentiable? Homework Help ✎

Clues 1 and 4 refer to the end behavior of *f*(*x*). Notice that there *f*(*x*) approaches ∞ in one direction, but approaches a horizontal asymptote in the other.

Clues 2 and 3 refer the slopes before and after *x* = 0. Notice that these limits describes the derivative, *f* '(*x*), not the actual function that you are graphing. Also notice that the limit from the left does not agree with the limit from the right, so *f*(*x*) is NOT differentiable at *x* = 1.