14) Find the equations of the tangent and normal to the given curves at the indicated points

d)  y = x^2\: \: at\: \: (0, 0)

Answers (1)

We know that Slope of the tangent at a point on the given curve is given  by  \frac{dy}{dx}
Given the equation of the curve
y = x^2
\frac{dy}{dx}= 2x
at point (0,0)
\frac{dy}{dx}= 2(0)^2 = 0
Hence slope of tangent is 0
Now we know that,
slope \ of \ normal = \frac{-1}{slope \ of \ tangent} = \frac{-1}{0} = -\infty
Now, equation of tangent at point (0,0) with slope = 0 is
y = 0
Similarly, equation of normal at point (0,0) with slope = -\infty is

\\y = x \times -\infty + 0\\ x = \frac{y}{-\infty}\\ x=0

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