Tangent公式問題

2009-12-22 10:51 pm

我之前上網搵到一條搵equation of tangent 既公式：y - f(a) = f '(a) (x-a)
我想問 ( a, f(a) ) 係 f(x) 同佢既tangent既相交點，咁f '(a)係乜野同埋點計???
可唔可以用以下既例子解析下???

The curve y = x^3 - 4x has a tangent that passes through point (1, -3) , find the equation of the tangent.

更新1:

唔該哂myisland8132既解答。我想問下咁以下呢條點計??? 因為(0, 2)唔係f(x)同佢既tangent既相交點, 以下呢條可以點用公式?? Given that the curve y = x^3 has a tangent that passes through point (0, 2),find the equation of the tangent.

更新2:

From mx+2=x^3, why m=3x^2 at the touching point????

回答 (1)

myisland8132

2009-12-22 11:03 pm

✔ 最佳答案

f '(a) 是f(x)在a點的導數。若果f(x)=x^n﹐則f'(x)=nx^(n-1)

The curve y = x^3 - 4x has a tangent that passes through point (1, -3) , find the equation of the tangent.

f(x)=x^3-4x,f'(x)=3x^2-4.when x=1,f'(x)=-1
So, the required equation is y+3=-(x-1) or x+y+2=0

2009-12-22 19:29:07 補充：
您用逆向思維。 a tangent that passes through point (0, 2) So y-2=mx. Sub. into y=x^3
mx+2=x^3. Since m=3x^2 at the touching point, 3x^3+2=x^3=>2x^3=-2 or x=-1

So m=3 and y-2=3x is the required tangent line

👍 0 👎 0