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.