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Ailyt2543
20.12.2019 •
Mathematics
Acurve has the slope 2x+3 at each point (x,y) on the curve. what is an equation for this curve if it passes through the point (1,2)
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Ответ:
∫f(x) = ∫2x + 3 dx
F(x) = x^2 + 3x + C
2 = (1)^2 + 3(1) + C
2 = 4 + C
C= -2
Therefore, the curve is F(x) = x^2 + 3x - 2
Proof: The derivative is the slope at every (x, y) point. The derivative of F(x) comes out to be 2x + 3, so we have found the curve. Plug in x = 1, and y = 2, so the conditions have been met.
Hope I helped.
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