Question

Let f(x)=2x−5. If h≠0, then the difference quotient can be simplified as (f(x+h)−f(x))/h=Ah+Bx+C, where A, B, and C are constants. (Note: It's possible for one or more of these constants to be 0.)

Find the constants.

Answer 1

The constants are A = 2, B = 0, and C = 0.

Step-by-step explanation:

To find the constants A, B, and C in the difference quotient (f(x+h)−f(x))/h=Ah+Bx+C for the function f(x)=2x−5, we need to substitute the given values and simplify the expression.

Let's substitute the values into the expression:

((2(x+h)−5)−(2x−5))/h=Ah+Bx+C

(2x+2h−5−2x+5)/h=Ah+Bx+C

(2h)/h=Ah+Bx+C

2=A+Bx+C

This shows that the constant A is 2, B is 0, and C is also 0.