How Do You Determine the T-line and N-line for f(x) = x*sqrt(5-x) at x = -4?

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Chocolaty
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Here's the question:
Given: f(x) = x*sqr(5-x)
Find: the equation (ax + by + c = 0) of T-line and N-line at x = -4

What's an N-line?
 
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Never heard of those terms, but if T-line is the tangent then N-line is the normal line (the line perpendicular to the tangent at x=-4) I suppose.

- Kamataat
 
it's your course, it's your definition, ask your teacher.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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