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Question
Find the slope of the tangent and the normal to the following curve at the indicted point y = 2x2 + 3 sin x at x = 0 ?
Solution
\[ y = 2 x^2 + 3 \sin x\]
\[ \Rightarrow \frac{dy}{dx} = 4x + 3 \cos x\]
When `x=0`
`y=2x^2+3sin x`
`=2(0)^2+3sin 0`
`=0`
\[\text { Now }, \]
\[\text { Slope of the tangent }= \left( \frac{dy}{dx} \right)_\left( 0, 0 \right) =4\left( 0 \right)+ 3 \cos 0=3\]
\[\text { Slope of the normal }=\frac{- 1}{\left( \frac{dy}{dx} \right)_\left( 0, 0 \right)}=\frac{- 1}{3}\]
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