### Home > CALC > Chapter 3 > Lesson 3.3.3 > Problem 3-117

Sketch a function

*f*(*x*) for which the following is true about its slope function*f*′(*x*)*.*Homework Help ✎For

*x*< −3,*f*′(*x*) > 0 and the slope is increasing.For −3 <

*x*< −1,*f*′(*x*) > 0 and the slope is decreasing.At

*x*= −1,*f*′(*x*)= 0.For

*x*> −1,*f*′(*x*) < 0 and the derivative is decreasing.

Be careful! The clues give information about *f* '(*x*), but you are asked to sketch *f*(*x*).

Translate: When *x* is greater than −3, *f*(*x*) is increasing and concave up.

Translate: When *x* is in between −3 and −1, *f*(*x*) is increasing and concave down.

Translate: When *x* is exactly −1, *f*(*x*) has reached a local maximum or minimum.

Translate: When *x* is greater than −1, *f*(*x*) is decreasing and concave down.

Remember that this graph is based on a slope statement. Without information about the exact *y*-values of *f*(*x*),the entire sketch can be shifted vertically up or vertically down.