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Nata [24]
3 years ago
13

(a) the curve with equation y2 = x3 + 3x2 is called the tschirnhausen cubic. find an equation of the tangent line to this curve

at the point (1, 2).

Mathematics
1 answer:
Inessa [10]3 years ago
7 0
Hello : 
y² =x^3+3x²
the derivate is : 2yy' = 3x²+6x
where x= 1 and y = 2
2(2)y' = 3(1)²+6(1)
4y' = 9
y' = 9/4
an equation at (1.2) is :  y = (9/4)(x-1)+2
y= (9/4)x-1/4

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\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
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\\ \quad \\
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\bf % template detailing
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\\\\
\bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\
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\left. \qquad  \right.  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\

\bf \bullet \textit{ vertical shift by }{{  D}}\\
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\bullet \textit{ period of }\frac{2\pi }{{{  B}}}

now, with that template in mind, let's see

\bf y=x^2\implies 
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y=(&1x&-0)^2\\
&B&C
\end{array}

so, just change C to +3, thus C/B is 3/1
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