Compute and simplify the difference quotient quotient
-f(x) = 5
A) 10x + 5h + 7
B) 15x - 7h + 14
C) 10x + 7

Question

Compute and simplify the difference quotient quotient 
-f(x) = 5 
A) 10x + 5h + 7 
B) 15x - 7h + 14 
C) 10x + 7

Quizplus · Accepted Answer

The difference quotient for f(x) is given by:

[(5(x + h) + 7) - (5x + 7)]/h

Simplifying the numerator, we get:

(5x + 5h + 7 - 5x - 7)/h

Simplifying further, we get:

(5h)/h = 5

Therefore, the difference quotient is simply 5, which means that the rate of change of f(x) with respect to x is a constant value of 5.

Comparing the given answer choices with our result, we see that only choice A matches. Therefore, the best choice is A.

Compute and Simplify the Difference Quotient Quotient