how do you calculate the angle of inclination of y=x^{2 }to the nearest degree?
please help!!!
A function does not have an "angle of inclination"! I assume you mean "the angle of inclination with the x-axis of the tangent to the curve $\displaystyle y= x^2$ at any point".
If $\displaystyle \theta$ is the angle the tangent line to y= f(x) makes with x-axis than $\displaystyle tan(\theta)= df/dx$.
The slope of the tangent line is found by evaluating the derivative of the function at the given x-coordinate.
$\displaystyle y'(1)=2(1)=2$
The slope $\displaystyle m$ of a line is related to its angle of inclination $\displaystyle \theta$ by $\displaystyle m=\tan(\theta)$.
Hence, the angle of inclination is $\displaystyle \theta=\tan^{-1}(2)\approx63^{\circ}$.