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Question

Find the equation of the tangent to the curve y=x7(x2)(x3) at the point where it cuts the x-axis.

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Solution

Note that on x- axis, y=0. So the equation of the curve, When y=0, gives x=7. Thus, the curve cuts the x-axis at (7,0), Now differentiating the equation of curve with respect to x, we obtain
dydx=1y(2x5)(x2)(x3) (Why?)
dydx]7,0=10(5)(4)=120

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