Lu J.

asked • 12/03/20

derivative f(x)=7x^2+x-2 at (0,-2)

Is there a certain order to when to plug things in to the standard formula?

Ashis J.

The question is not entirely accurate, you will be given a function f(x) and you have to find its derivative and then find the value of x when say f '(x) = 0 or maybe 1 or 2. Here, it says find the derivative at (0, -2) where x = 0 and y = -2. Maybe you are trying to say that derivative of f(x), i.e. f '(x) =7x^2 + x - 2. If that is so, then its simple and I will solve it now.
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12/03/20

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Ashis J. answered • 12/03/20

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Derivative of f(x), i.e. f '(x) = 7x^2 + x -2, let us integrate this or in other words find the anti-derivative. We get ∫f '(x) dx = ∫(7x^2 + x - 2)dx = 7/3x^3 + 1/2x^2 + 2x + c (where c = integration constant). Now, our point has (0,-2) which means y at f(x) where x = 0 has a value -2. So, y = f(x) = 7/3x^3 + 1/2x^2 + 2x + c. Now, put x = 0 and y = -2 and solve for c, we get -2 = 0 + 0 + 0 + c => c = -2. Therefore, f(x) = 7/3x^3 + 1/2x^2 + 2x - 2. (Ans).

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Milun P.

For some reason, I am not able to submit my answer, so I will comment on this one. The derivative of f(x) is f'(x) = 14x+1. The derivative of f(x) at point (0,-2) is f'(0) = 14*0+1 = 1. This answer is the slope of the tangent of function f(x) at point (0,-2).
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12/04/20

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