Asked Jun 8, 2019

Find the indicated difference quotient and simplify your answer.

f (x) = x 3 +3x, f (x +h)− f (x) /h , h does not equal 0 

f (x) = 1 /x2 , g (x)− g (3) /x −3 , x does not equal 3.

f (t) = 1 / t −2 , f (t)− f (1)/ t −1 , t does not equal 1.


Expert Answer

Step 1

Using given f(x) first find f(x+h).


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f(x) x 3x f(xh) (xh)3 +3(x+h) f(xh)x 3x h+3xh +h +3x+3h

Step 2

Plugged the expression of f(x) and f(x+h) in the difference quotient and simplified. [h does not equal 0]

Answer: 3x^2+3xh+h^2+3


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f(x+h)-f(x) h (x3 +3xh+3xh +h'+3x+ 3h)-(x +3x) 3x2h+3xhh3h h h(3x2 3xh h3) h = 3x2 +3xh+h 3

Step 3

Using given g(x) fir...


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1 g(x) x 1 g(3) 32 1 g(3) 9


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