0
What else can I help you with?
What is a derivative graph?
A derivative graph tracks the slope of a function.
What are the uses of derivatives?
A derivative of a function represents that equation's slope at any given point on its graph.
How do you find critical value for a total revenue function?
If it is a differentiable function, you find the value at which its derivative is 0. But in general, you can plot it as a line graph and see where it peaks.
How do you graph function g?
use y = g(x) make a table of y values for several x values Find max/min values using derivative. graph the ordered pairs.
What is concavity of a function?
Just as the slope of the tangent line to the graph of f at the point (x, f(x)) describes the behavior of the function, concavity describes the behavior of the slope. As x increases (graph goes from left to right), one of the following is true:Concavity is positive, so the slope slowly increases.Concavity is negative, so the slope slowly decreases.Concavity is equal to zero, so the slope is constant.Again, remember that concavity directly affects the slope, NOT the function itself. I mean this in the sense that concavity affects slope affects function.Mathematically speaking, you can find the concavity at a certain point by taking the derivative of the derivative of the function (accurately called the second derivative, f''). So, when you take the derivative of a function, you get the first derivative, f' (describing slope), and the derivative of that is the second derivative (describing the concavity).Last but not least, here is a handy way to find the concavity of a function by looking at its graph:Concavity is positive when the graph turns up, like a smiling emoticon (look at a graph of f(x) = x2 for an example).First observe that f'(x) = 2x.We see that f' < 0 when x < 0 and f' > 0 when x > 0. So that the graph is decreasing on the negative real axis and the graph is increasing on the positive real axis.Next observe that f''(x) = 2.Thus, f'' > 0 at all points. Thus the graph is concave up everywhere.Finally observe that the graph passes through the origin.Concavity is negative when the graph turns down, like a frowning emoticon (look at a graph of f(x) = -x2 for an example).First observe that f'(x) = -2x.We see that f' > 0 when x < 0 and f' < 0 when x > 0. So that the graph is increasing on the negative real axis and the graph is decreasing on the positive real axis.Next observe that f''(x) = -2.Thus, f'' < 0 at all points. Thus the graph is concave down everywhere.Finally observe that the graph passes through the origin.Look at the graph of f(x) = x3First observe that f'(x) = 3x2.Thus, f' ≥ 0 everywhere. The function is always increasing.Next observe that f''(x) = 6x.Thus, f'' < 0 when x < 0 and f'' > 0 when x > 0. So the graph is concave down on the negative real axis and concave up on the positive real axis.Finally observe that the graph passes through the origin.Concavity is zero when the graph is linear OR at a point where it stops turning up and starts turning down, and vice versa.
How does the graph of an exponential function differ from the graph of a linear function and how is the rate of change different?
The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.
What is a derivative graph?
A derivative graph tracks the slope of a function.
Where the graph of a function equals the value zero?
you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.
What is the highest point on a graph?
The highest point on a graph is when the derivative of the graph equals 0 or the slope is constant.
What is the difference between nonlinear and linear functions?
Linear function:No variable appears in the function to any power other than 1.A periodic input produces no new frequencies in the output.The function's first derivative is a number; second derivative is zero.The graph of the function is a straight line.Non-linear function:A variable appears in the function to a power other than 1.A periodic function at the input produces new frequencies in the output.The function's first derivative is a function; second derivative is not zero.The graph of the function is not a straight line.
What characteristics of the graph of a function by using the concept of differentiation first and second derivatives?
If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.
What does it mean for a function when the graph of the derivative crosses the x-axis?
This means that the function has reached a local maximum or minimum. Since the graph of the derivative crosses the x-axis, then this means the derivative is zero at the point of intersection. When a derivative is equal to zero then the function has reached a "flat" spot for that instant. If the graph of the derivative crosses from positive x to negative x, then this indicates a local maximum. Likewise, if the graph of the derivative crosses from negative x to positive x then this indicates a local minimum.
What is an increment on a graph?
a thing on math
How do you graph the slope of a function?
For example, if the slope at a certain point is 1.5, you can draw a line that goes through the specified point, with that slope. The line would represent the slope at that point. If you want to graph the slope at ALL POINTS, take the derivative of the function, and graph the derivative. The derivative shows the slope of a function at all points.
How is the function differentiable in graph?
If the graph of the function is a continuous line then the function is differentiable. Also if the graph suddenly make a deviation at any point then the function is not differentiable at that point . The slope of a tangent at any point of the graph gives the derivative of the function at that point.
What does the derivative of a function mean?
The derivative of a function is another function that represents the slope of the first function, slope being the limit of delta y over delta x at any two points x1,y1 and x2,y2 on the graph of the function as delta x approaches zero.
How do you graph trigonometric functions?
You find the average rate of change of the function. That gives you the derivative on different points of the graph.
