Slope angle
With the derivation you can also determine the slope angle at a point $x$.
!
Remember
The slope angel $\alpha$ of a function $f$ at the point $x$ is:
$\alpha=\arctan(f'(x))$
$\alpha=\arctan(f'(x))$
Example
Calculate the slope angle of the function $f(x)=x^2$ at $x=1$.
Antiderivative: $f(x)=x^2$Derivative: $f'(x)=2x$
Insert:
$\alpha=\arctan(f'(x))$
$\alpha=\arctan(f'(1))$
$f'(1)=2\cdot1=2$
$\alpha=\arctan(2)\approx63,43°$
i
Hint
Frequently, calculators use $\arctan$ instead of $\tan^{-1}$. Both methods are the same.