Question

The figure shows the graph of f(x)=4+x/x+3, along with it's tangent line at the point (0,4). What is f'(0)?

Answer 1

Since we know the tangen line:

$y=\frac{1}{3}x+4$

then f ^prime evaluated at zero is the same as evaluate this last equation at x=0, that is,

$f\text{´}(0)=\frac{1}{3}(0)+4$

which gives

$f^{\prime}(0)=4$

then, the answer is 4.

Lets compute the derivative of our given function:

then, f^prime at zero is equal to

then, the answer is 1/3. Then, the given line doesnt correspond with the derivative at x=0