f(x)=6x–4 and f(–1)=2 and f(–1)=–5. What isf(x) and what is f(3)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to consider the reverse of differentiation, meaning that you need to integrate `f'(x)`  to find `f(x)`  such that:

`int f'(x)dx = int (6x-4)dx`

You need to split the integral into simpler integrals such that:

`int (6x-4)dx = int (6x)dx - int (4)dx`

`int (6x-4)dx = 6*x^2/2 - 4x + c`

`int (6x-4)dx = 3x^2 - 4x + c`

Hence,integrating f'(x) yields`f(x) = 3x^2 - 4x + c`

You need to find c using the information `f(-1) = 2`  such that

`2 = 3 + 4 + c =gt c = 2 - 7 =gt c = -5`

Hence, the integrating f'(x) under given conditions yields `f(x) = 3x^2 - 4x - 5.`

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate f(3), hence, you need to substitute 3 for x in equation of f(x) such that:

`f(3) = 3*9 - 4*3 - 5 =gt f(3) = 27 - 12 - 5 =gt f(3) = 10`

Hence, evaluating the value of function at x=3 yields f(3) = 10.

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