Find the equation of the normals to the curve y = x³ + 2x + 6 which are parallel to the line x + 14y + 4 = 0.

Question

Find the equation of the normals to the curve y = x³ + 2x + 6 which are parallel to the line x + 14y + 4 = 0.

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Maya 3 weeks 2021-10-04T01:05:35+00:00 2 Answers 0 views 0

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    0
    2021-10-04T01:07:05+00:00

    Answer:

    .

    Step-by-step explanation:

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    ans:

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    0
    2021-10-04T01:07:10+00:00

    Equation of the curve is y = x3 + 2x + 6

    Slope of the normal at point (x,y) = minus fraction numerator 1 over denominator open parentheses begin display style dy over dx end style close parentheses end fraction

    On substitution, we get

    Slope of the normal = minus fraction numerator 1 over denominator 3 straight x squared plus 2 end fraction space space space space space….. left parenthesis 1 right parenthesis

    Normal to the curve is parallel to the line x + 14y + 4 = 0.

    i.e yequals minus 1 over 14 equals minus fraction numerator 1 over denominator 3 straight x squared plus 2 end fraction

    So the slope of the line is the slope of the normal.

    Slope of the line is minus 1 over 14 equals minus fraction numerator 1 over denominator 3 straight x squared plus 2 end fraction

    When x = 2, y = 18 and when x = -2, y =-6

    Therefore, there are two normal to the curve y = x3 + 2x + 6.

    Equation of normal through point (2,18) is given by:

    Therefore, the equation of normal to the curve are x+14y-254 = 0

    and x + 14y + 86 = 0

    hope it helps plz mark me as BRILLIANT ❤️….

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