Use this distinction quotient calculator to locate how much a function modifications on common over a selected c language. Our device presentations stepwise calculations to degree the slope of the secant line which passes via two points.
"distinction quotient is a mathematical expression used to degree the slope of the secant line among the two one-of-a-kind factors on the graph of a feature."
In easy words, the distinction quotient measures the charge of trade of a function f(x) for x in a given c language [x, x + h].
The difference quotient equation measures the approximated shape of the spinoff as:
f(x) = f(x + h) – f(x) h
Where:
The difference quotient components affords an approximation of a characteristic's derivative.
Observe these steps to decide difference quotients:
Example:
Find the difference quotient for the following function:
F(x) = 3x3 + 5x
Solution:
To find f(x + h), substitute x + h for x:
f(x + h) = 3(x + h)3 + 5(x + h)
Then,
= ((x + h)3 + 5(x + h)) – (3x3 + 5x) h
= (x + h)3 + 5x + 5h – 3x3 – 5x h
= 3h(x2 + 2xh + h2) + 5h h
f(x) = 3x3 + 5x = 3h(x2 + 2xh + h2) + 5h
Thus, the difference quotient for f(x) = 3x3 + 5x is \( 3h(x^2 + 2xh + h^2) + 5h \). For quick results, use our simplified difference quotient calculator.