DIFFERENTIATION RULES

👨🏻‍🏫 學術台數學

Peng

2008-10-12 11:12 pm

A curve passes through the point (0,5) and has the property that the slope of the curve at every point is twice the y-coordinate of . What is the equation of the curve?

更新1:

更正題目: A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?

回答 (1)

Audrey Hepburn

2008-10-12 11:24 pm

✔ 最佳答案

The slope of the curve at any point P(x , y) is twice the y-coordinate of P.

i.e. dy/dx│P(x , y) = 2y

dy/dx = 2y

∫dy / (2y) = ∫dx

1/2 lny = x + C, where C is a constant

y = Ae2x, where A is a constant

Since the curve passes through (0 , 5)

So, 5 = A(1), A = 5

Hence, equation of the curve: y = 5e2x

參考: Myself~~~

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