Question

Is `f(x)=tanx` increasing or decreasing at `x=0`?

Answer 1

Increasing

Explanation:

If `f'(0)>0`, the function is increasing at that point. If `f'(0)<0`, the function is decreasing at that point.

`f'(x)=sec^2x`

`f'(0)=sec^2(0)=1/(cos^2(0))=1`

Since `1>0`, the function is increasing at that point.

Check the graph:

graph{tanx [-6.24, 6.247, -3.12, 3.12]}