The equation of a curve is $$\(2 \mathrm{e}^{2 x} y-y^{3}+4=0\)$$. The curve passes through the point $$\((0,2)\)$$. Find the equation of the tangent to the curve at this point, giving your answer in the form $$\(a x+b y+c=0\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_22 Year：2020 Question No：5(b)
Answer:
Substitute 0 and 2 to find gradient of tangent
Attempt to find equation of tangent through \((0,2)\) with numerical gradient
Obtain \(4 x-5 y+10=0\) or equivalent of required form
Attempt to find equation of tangent through \((0,2)\) with numerical gradient
Obtain \(4 x-5 y+10=0\) or equivalent of required form
Knowledge points:
2.4.3 find and use the first derivative of a function which is defined parametrically or implicitly.
Solution:
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