Given:f(x) = 5-x-3x²

Compute: f(x+h) – f(x)

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It is given that f(x) = 5 - x - 3x^2

f(x+h) - f(x)

=> 5 - (x+h) - 3(x+h)^2 - (5 - x - 3x^2)

=> 5 - x - h - 3x^2 - 3h^2 + 6xh - 5 + x + 3x^2

=> - h - 3h^2 + 6xh

The required value of f(x+h) - f(x) = - h - 3h^2 + 6xh

Calculate f(x+h)=5-(x+h)-3(x+h)^2

Use formula (a+b)^2=a^2+2ab+b^2 to expand (x+h)^2.

(x+h)^2 = x^2 + 2xh + h^2

Multiply by 3 => 3x^2 + 6xh + 3h^2

Open the brackets:

f(x+h)=5 - x - h - 3x^2 - 6xh - 3h^2

Subtract f(x) from f(x+h):

5 - x - h - 3x^2 - 6xh - 3h^2 - 5 + x + 3x^2

Reduce opposite terms:

-h - 6xh - 3h^2

**ANSWER: f(x+h)-f(X)= -h - 6xh - 3h^2**

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