Question

(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).

Answer 1

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