Compute the difference quotient, StartFraction f (x plus h )minus f (x )Over h EndFraction f(x+h)−f(x) h, for the function f (x )equals 3 x squaredf(x)=3x2, and simplify.

The difference quotient for is .

Step-by-step explanation:

The difference quotient is a formula that computes the slope of the secant line through two points on the graph of f. These are the points with x-coordinates x and x + h. The difference quotient is used in the definition the derivative and it is given by

So, for the function the difference quotient is:

To find , plug instead of

Finally,

The difference quotient for is .