Final answer:
To evaluate f(x+h)-f(x)/h for the function f(x)=6x², substitute the values of f(x+h) and f(x), expand and simplify the expression.
Step-by-step explanation:
To evaluate f(x+h)-f(x)/h for the function f(x)=6x², we substitute the values of f(x+h) and f(x) into the expression.
Substituting f(x+h)=6(x+h)² and f(x)=6x² gives us:
6(x+h)²-6x²/h
Expanding (x+h)² gives us x²+2xh+h², so the expression becomes:
6(x²+2xh+h²)-6x²/h
Simplifying further, we get:
6x²+12xh+6h²-6x²/h
The 6x² terms cancel out, leaving us with:
12xh+6h²-6x²/h
This is the evaluated expression for f(x+h)-f(x)/h.