Increasing and decreasing Problem set A

The graph shows y = f(x), a parabola with its highest point at (2, 4). Write the values of x for which f is increasing.

The graph shows y = f(x), a cubic with turning points at x = −2 and x = 1. Write down the values of x for which f is:

1. (a) increasing;
2. (b) decreasing.

The graph shows y = f(x) for 0 ≤ x ≤ 360, where x is in degrees. It has a maximum at (90, 4) and a minimum at (270, −4).

1. (a) Write down the values of x for which f is increasing.
2. (b) Write down the values of x for which the gradient of the graph is zero.

The line shown is the tangent to the curve at P(7, 9). It passes through (4, 0) and (6, 6).

1. (a) Find the gradient of the curve at P.
2. (b) Write down the value of x at which the gradient of the curve is zero.

The graph shows the height h metres of a cyclist above the valley floor after riding d kilometres along a route, for 0 ≤ d ≤ 6. The turning points are (2, 20) and (4, 16).

1. (a) For which values of d is the cyclist going uphill?
2. (b) State the gradient of the graph at d = 4 and say what it tells you about the road.

A function f is defined for all x. It is increasing for x < −1, decreasing for −1 < x < 3 and increasing for x > 3. Describe the graph of y = f(x): where the gradient is zero, what kind of turning points they are, and the overall shape.

The graph shows y = f(x), a quartic with a W shape.

1. (a) Write down the values of x for which f is increasing.
2. (b) Write down the values of x at which the gradient is zero.