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For the function f(x) = 7/2x-16, what is the difference quotient for all nonzero values of h?

User Tiziana
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2 Answers

1 vote

Answer:

It is A.

Explanation:

Just took the test

User Lincetto
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6 votes

Answer:


(f(x + h) - f(x))/( h) = (7)/(2)

Explanation:

Given


f(x) = (7)/(2)x - 16

Required

The difference quotient for h

The difference quotient is calculated as:


(f(x + h) - f(x))/( h)

Calculate f(x + h)


f(x) = (7)/(2)x - 16


f(x+h) = (7)/(2)(x+h) - 16


f(x+h) = (7)/(2)x+ (7)/(2)h- 16

The numerator of
(f(x + h) - f(x))/( h) is:


f(x + h) - f(x) = (7)/(2)x+ (7)/(2)h- 16 -((7)/(2)x - 16)


f(x + h) - f(x) = (7)/(2)x+ (7)/(2)h- 16 -(7)/(2)x + 16

Collect like terms


f(x + h) - f(x) = (7)/(2)x -(7)/(2)x + (7)/(2)h- 16 + 16


f(x + h) - f(x) = (7)/(2)h

So, we have:


(f(x + h) - f(x))/( h) = (7)/(2)h / h

Rewrite as:


(f(x + h) - f(x))/( h) = (7)/(2)h * (1)/(h)


(f(x + h) - f(x))/( h) = (7)/(2)

User Techvice
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