Find the The Slopes of the tangent and the normal to the following curves at the indicated points :

y = 2x² + 3 sin x at x = 0

Given:

y = 2x² + 3sinx at x = 0

First, we have to find of given function, f(x),i.e, to find the derivative of f(x)

(xⁿ) = n.x^{n – 1}

The Slope of the tangent is

⇒ y = 2x² + 3sinx

⁼ 2(x²) + 3(sinx)

= 22x^{2 – 1} + 3(cosx)

(sinx) = cosx

= 4x + 3cosx

Since, x = 2

⇒ _{x = 0} = 40 + 3cos(0)

cos(0) = 1

⇒ _{x = 0} = 0 + 31

⇒ _{x = 0} = 3

The Slope of the tangent at x = 0 is 3

⇒ The Slope of the normal =

⇒ The Slope of the normal =

⇒ The Slope of the normal =