Q1 of 149 Page 16

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.xn – 1


The Slope of the tangent is


⇒ y = 2x2 + 3sinx


= 2(x2) + 3(sinx)


= 22x2 – 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 =


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