Question

Find the difference quotient for f(x) = 5x² - x/6.

a) (5h² - h)/6h
b) (5h - 1)/6
c) (5h + h²)/6h
d) (5 - h)/6

Answer 1

The difference quotient for the function f(x) = 5x² - x/6 is (5h² - h)/6h

Step-by-step explanation:

The difference quotient for the given function, f(x) = 5x² - x/6, can be found by subtracting the value of the function at x+h from the value of the function at x, and then dividing the result by h. This can be expressed as:

(f(x+h) - f(x))/h

To calculate this, we need to substitute x+h and x into the function and simplify:

f(x+h) = 5(x+h)² - (x+h)/6

f(x) = 5x² - x/6

Now, we can subtract f(x) from f(x+h) and divide the result by h:

((5(x+h)² - (x+h)/6) - (5x² - x/6))/h

This simplifies to:

(5h² - h)/6h