Question

Please walk through this with me. I need to find the derivative and also the tangent line of each equation

Answer 1

We have;

Power law;

`(d(x^(n)))/(dx)=nx^(n-1)`

`f(x)=√(x+4)`
`f^(\prime)(x)=(1)/(2)(x+4)^{-(1)/(2)}=(1)/(2√(x+4))`

ii. At P (0,2);

`f^(\prime)(0)=(1)/(2√(4))=(1)/(4)`

The equation of the tangent line is;

`\begin{gathered} y-2=(1)/(4)(x-0) \\ 4(y-2)=x \\ 4y-8=x \\ The\text{ equation of the line is thus }4y-x-8=0 \end{gathered}`

b.

`\begin{gathered} f(x)=x^2+x \\ f^(\prime)(x)=2x+1 \\ f^(\prime)(1)=2(1)+1=3 \end{gathered}`

The equation of the tangent line is;

`\begin{gathered} y-2=3(x-1) \\ y-2=3x-3 \\ The\text{ equation of the line is thus }y-3x+1=0 \end{gathered}`