Let f be a function and a be the given point you are considering. Then,
f(x) - f(a)
---------------
(x-a)
is the difference quotient. If the limit as x approaches a exists, then the function is differentiable at a, or we say the derivative exists at a. If that limit does not exist, then the derivative does not exist at that point.
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If the second derivative of a function is zero, then the function has a constant slope, and that function is linear. Therefore, any point that belongs to that function lies on a line.
The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.
A function is differentiable at a point if the derivative exists there.
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.
the deivative of a function is the gradient, at a point if you can sub in the x coordinate for that point
By taking the derivative of the function. At the maximum or minimum of a function, the derivative is zero, or doesn't exist. And end-point of the domain where the function is defined may also be a maximum or minimum.
A derivative of a function represents that equation's slope at any given point on its graph.
A derivative of a function represents that equation's slope at any given point on its graph.
To calculate the derivative of a mathematical function using the scipy differentiation function, you can use the scipy.misc.derivative function. This function takes the mathematical function, the point at which you want to calculate the derivative, and the order of the derivative as input parameters. It then returns the numerical value of the derivative at that point.
If the second derivative of a function is zero, then the function has a constant slope, and that function is linear. Therefore, any point that belongs to that function lies on a line.
The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.
A function is differentiable at a point if the derivative exists there.
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.
In math, the derivative of a function is the graph of the function's slope, or the rate of change of a function at a given point. In other senses, it means something that is derived, or comes from, something else.
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.
the deivative of a function is the gradient, at a point if you can sub in the x coordinate for that point
There are several uses. For example: * When analyzing curves, the second derivative will tell you whether the curve is convex upwards, or convex downwards. * The Taylor series, or MacLaurin series, lets you calculate the value of a function at any point... or at least, at any point within a given interval. This method uses ALL derivatives of a function, i.e., in principle you must be able to calculate the first derivative, the second derivative, the third derivative, etc.