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Question

Find the equation of the tangent and the normal to the following curves at the indicated points.
y=x4bx3+13x210x+5 at (0,5).

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Solution

Tangent=y+10x5=0
Normal=x10y+50=0.
The equation of the curve is y=x4bx3+13x210x+5.
dydx=4x33bx2+26x10
(dydx)(0,5)=10
The equation of tangent at (0,5) is
y5=(dydx)(0,5)(x0)
y5=10(x0)
10x+y5=0
The equation of the normal at (0,5) is
y5=1(dydx)(0,5)(x0)
y5=110(x0)
x10y+50=0.

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