f(x+h)-f(x)/h for f(x)= 4x+9 and simplify.
f(x+h)-f(x)/h
= (4(x+h) + 9 - (4x+9))/h
= 4x + 4h + 9 - 4x - 9)/h
= 4h/h
= 4 , h not equal to zero
Thank you for the help!
To find the function f(x+h) for f(x) = 4x + 9, we substitute (x+h) into the function in place of x:
f(x+h) = 4(x+h) + 9
= 4x + 4h + 9
Now, let's find the difference quotient, which is essentially the slope of the function between two points.
Difference quotient = [f(x+h) - f(x)] / h
Substituting the values:
[f(x+h) - f(x)] / h = [(4x + 4h + 9) - (4x + 9)] / h
Simplifying further:
= (4x + 4h - 4x - 9) / h
= 4h / h
= 4
Therefore, the simplified form of the difference quotient for the given function f(x) = 4x + 9 is 4.