Determine an equation for the tangent to the graph of f(x) at point P.

Question

Determine an equation for the tangent to the graph of f(x) at point P.

Use of CAS tool allowed.

a) f(x)= 3/(1+√x) , P(4, 1)

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b) f(x)= √(5-x^2 ) , P(1, 2)

Answer 1

Since you are allowed to use a CAS tool, there is not much to do here.

Here is one such tool: a), and b)

Answer 2

Hint: Equation of tangent line of $f$ at $(x_0,y_0)$ is $$y-y_0=m(x-x_0)$$ where

a) $x_0=4,y_0=1$ and $m=f'(4)$

b) $x_0=1,y_0=2$ and $m=f'(1)$