Difference quotient for f at x=a
The graph of f is concave downward on the interval a
The difference quotient for a function f at x=a is a mathematical expression that represents the slope of the secant line between two points on the graph of the function. More specifically, it is defined as:
[f(a+h) – f(a)] / h
where h is a small change in the value of x (typically approaching zero), and (a,h) and (a+h, f(a+h)) are two points on the graph of the function.
Geometrically, this expression represents the slope of the line that passes through the points (a,f(a)) and (a+h, f(a+h)) as h approaches zero. This is equivalent to the instantaneous rate of change of f at x=a, which is also known as the derivative of f at x=a. The difference quotient is an important concept in calculus and is commonly used to calculate derivatives and slopes of tangent lines.
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The difference quotient for a function f at x=a is a mathematical expression that represents the slope of the secant line between two points on the graph of the function. More specifically, it is defined as:
[f(a+h) – f(a)] / h
where h is a small change in the value of x (typically approaching zero), and (a,h) and (a+h, f(a+h)) are two points on the graph of the function.
Geometrically, this expression represents the slope of the line that passes through the points (a,f(a)) and (a+h, f(a+h)) as h approaches zero. This is equivalent to the instantaneous rate of change of f at x=a, which is also known as the derivative of f at x=a. The difference quotient is an important concept in calculus and is commonly used to calculate derivatives and slopes of tangent lines.
More Answers:
Mastering The Product Rule Of Differentiation: How To Easily Derive Constant Multiplication In MathMastering Derivatives: The Simple Technique Of Finding The Derivative Of Sum Or Difference Of Two Functions
How F(X) < 0 Impacts The Concavity Of F(X) Within [A, B] Interval