Using the difference quotient to find M-sec for h=0.5 at x=1.
f(x)=2x+5
difference quotient-f(x+h)-f(x)/h
[2(1+.5) + 5 - (2(1)+5)]/.5
= [3+5 - (2+5)]/.5
= 1/.5
= 2
To find the difference quotient, we need to calculate the value of f(x+h) and f(x) for the given function and plug them into the formula.
Given:
f(x) = 2x + 5
h = 0.5
x = 1
First, let's calculate f(x+h) by substituting x+h into the function:
f(x+h) = 2(x+h) + 5
= 2x + 2h + 5
Next, let's calculate f(x):
f(x) = 2x + 5
Now, we can plug these values into the difference quotient formula:
M-sec = [f(x+h) - f(x)] / h
= [2x + 2h + 5 - (2x + 5)] / h
= [2(x+h) + 5 - 2x - 5] / h
= [2x + 2h + 5 - 2x - 5] / h
= [2h] / h
Simplifying the expression, we find that:
M-sec = 2
Therefore, the value of M-sec for h=0.5 at x=1 is 2.