Find the equation of the tangent line to the graph of x2 + xy + 2y2 = 28 at the

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Explanation / Answer

It is given that y=x^3. therefore, when x=4, y=4^3 ie. y=64. dy/dx=3x^2 a) The slope of the tangent(say m) is given by dy/dx|x=4 (meaning-> dy/dx when x=4) // you should be knowing that! therefore, dy/dx= 3x^2 = 3(4)^2 = 3*16 = 48. The equation of the tangent is given by y-y1 = m(x-x1) (the formula that u were supposed 2 learn in equivalent grade or equivalent) Substituting in this formula, we get y-64=48(x-4) That is the equation of the tangent. b) The slope of the normal (say M) is given by M=-1/m // m is the slope of the tangent Therefore, the slope of the normal is (-1/48). Substituting in the formula y-y1=M(x-x1) will again fetch you the equation of the normal. Therefore, the equation of the normal is y-64=(-1/48)*(x-4) (This can be further simplified by your self if you feel the need. But this much would be quiet enough)

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