?Find equations of the tangent line and normal line to the curve at the given point.y =

Step 1 of 2

The given data is,

\(y=x^{\frac{3}{2}},\left(x_{1}, y_{1}\right)=(1,1)\)

To find the equation of tangent at given point \((1, 1)\), first find the slope of the given equation that should be the derivative of the given equation.

The derivative is given as,

\(\begin{aligned} y & =x^{\frac{3}{2}} \\ y^{\prime} & =\frac{3}{2} x^{\frac{1}{2}} \\ y^{\prime}(1) & =\frac{3}{2} \end{aligned}\) 

Therefore, the equation of the tangent will become at the point \((1, 1)\) is

\(\begin{aligned} y-1 & =\frac{3}{2}(x-1) \\ y & =1+\frac{3}{2} x-\frac{3}{2} \\ y & =-\frac{1}{2}+\frac{3}{2} x \end{aligned}\)

Thus, the equation is \(y=-\frac{1}{2}+\frac{3}{2} x\)