Using the difference quotient find M-sec for h=0.5 at x=1.
f(x)=2x+5
difference quotient-f(x+h)-f(x)/h
To find the difference quotient, which represents the instantaneous rate of change of a function, in this case, f(x) = 2x + 5, we need to substitute the given values for h and x into the difference quotient formula.
The difference quotient formula is: f(x+h) - f(x) / h.
Now, let's calculate f(x+h) and f(x) first:
f(x+h) = 2(x+h) + 5
= 2x+2h + 5
f(x) = 2x + 5
Substituting these values into the difference quotient formula:
Difference quotient = (2x+2h + 5 - (2x + 5)) / h
Next, simplify the expression:
Difference quotient = (2x + 2h + 5 - 2x - 5) / h
= (2h) / h
= 2
Therefore, the difference quotient for h = 0.5 at x = 1 is 2.