Problem 2 : (a) sketch the graph of the function f (x) = x 2 3 . (b) find the domain and range of the function. (c) find the intervals on which f increases and decreases. problem 3 : the graph of the function shown below has domain [−1, 6]. (a) find the largest interval on which f is increasing. (b) find the largest interval on which f is. Stationary points, increasing and decreasing functions revision guide. examples: 1. prove that the curve y = x 3 3x 2 3x 2 has only one stationary point. show that the stationary point is a point of inflection. 2. show that the curve y = 4x x 4 has only 1 stationary point. determine the nature of this point. 3.
Click here for answers. practice questions. previous: fm equation of a tangent to a circle questions. next: fm factorising quadratics questions. the corbettmaths practice questions on increasing decreasing function for level 2 further maths. 3. shown below is the graph of the point (2, 18) is a maximum point and the point (7, 5) is a minimum point. write down the range of values of x for which is an decreasing function. The graph of a linear function is a line. the slope of the line can provide useful information about the functional relationship between the two types of quantities: • a linear function whose graph has a positive slope is said to be an increasing function. • a linear function whose graph has a negative slope is said to be a decreasing function. Constant functions. a constant function is a horizontal line: lines. in fact lines are either increasing, decreasing, or constant. the equation of a line is: y = mx b. the slope m tells us if the function is increasing, decreasing or constant:.
The graph of a linear function is a line. the slope of the line can provide useful information about the functional relationship between the two types of quantities: • a linear function whose graph has a positive slope is said to be an increasing function. • a linear function whose graph has a negative slope is said to be a decreasing function. Constant functions. a constant function is a horizontal line: lines. in fact lines are either increasing, decreasing, or constant. the equation of a line is: y = mx b. the slope m tells us if the function is increasing, decreasing or constant:. Definition. increasing and decreasing functions. function f is increasing on an interval i if and only if: for all x1; x2 2 i, x1 < x2 =) f(x1) < f(x2) function f is decreasing on an interval i if and only if: 2 2 i, x1 < x2 =) f(x1) > f(x2)exampleproblem: identify the open intervals on which the function gra. solution:. (a) find the intervals on which g(x) is increasing and the intervals on which g(x) is decreasing. (b) find the intervals on which g(x) is concave up and the intervals on which g(x) is concave down. solutions: to determine where f(x) is increasing or decreasing, it is enough to determine where g0(x) is postive or negative. now, g0(x) = (x 1)(x 4.
Comments are closed.