How do you determine if a graph is concave up or down?
How do you determine if a graph is concave up or down?
A graph is said to be concave up at a point if the tangent line to the graph at that point lies below the graph in the vicinity of the point and concave down at a point if the tangent line lies above the graph in the vicinity of the point.
How do you explain concavity?
Concavity relates to the rate of change of a function’s derivative. A function f is concave up (or upwards) where the derivative f′ is increasing. This is equivalent to the derivative of f′ , which is f′′f, start superscript, prime, prime, end superscript, being positive.
What does it mean if the derivative is equal to zero?
The first derivative of a point is the slope of the tangent line at that point. When the slope of the tangent line is 0, the point is either a local minimum or a local maximum. Thus when the first derivative of a point is 0, the point is the location of a local minimum or maximum.
How do you interpret the second derivative?
- The Meaning of the Second Derivative.
- The second derivative of a function is the derivative of the derivative of that function.
- dx2 .
- tells us if the first derivative is increasing or decreasing.
- dx2 (p) > 0 at x = p, then f(x) is concave up at x = p.
- • if d2f.
- dx2 (p) < 0 at x = p, then f(x) is concave down at x = p.
What does derivative graph tell you?
The derivative of a function f is a function that gives information about the slope of f. The derivative tells us if the original function is increasing or decreasing. The second derivative gives us a mathematical way to tell how the graph of a function is curved.
How do you graph a linear equation?
If you know an equation is linear, you can graph it by finding any two solutions. ( x 1 , y 1 ) and ( x 2 , y 2 ) , plotting these two points, and drawing the line connecting them.
What is the difference between a graph and an equation?
Graphs are used to show a relatioship between x and y values. This relationship can be written as an equation. A straight line graph is made up of a gradient, denoted as M which determines the steepness and an intercept, denoted as C, which determines where the line crosses the y axis. A graph is a visual representation of a continuous function.
Can you graph a quadratic equation?
You can graph a Quadratic Equation using the Function Grapher, but to really understand what is going on, you can make the graph yourself. Read On! It is a parabola.
What is the relationship between X and Y on a graph?
Graphs are used to show a relatioship between x and y values. This relationship can be written as an equation. A straight line graph is made up of a gradient, denoted as M which determines the steepness and an intercept, denoted as C, which determines where the line crosses the y axis.