### Home > CALC > Chapter Ch3 > Lesson 3.4.2 > Problem 3-164

3-164.

Draw the graph of

*f*(*x*) given the following information about its slope function,*f*(*x*). Homework Help ✎*f*′(*x*) > 0 on 1 <*x*< 4*f*′(*x*) < 0 on*x*< 1 and*x*> 4*f*′(*x*) = 0 for*x*= 1,*x*= 4

Notice that the clues describe *f* '(*x*), yet you are asked to sketch *f*(*x*).

*f* '(*x*) > 0 on 1 < *x* < 4

Translate: *f*(*x*) is increasing between *x* = 1 and *x* = 4.

*f* '(*x*) < 0 on *x* < 1 and *x* > 4

Translate: *f*(*x*) is decreasing before *x* = 1 and after *x* = 4.

*f* '(*x*) = 0 for *x* = 1, *x* = 4

Translate: *x* has reached a local maximum or local minimum at *x* = 1 and *x* = 4.