Question

angle formed by the positive y-axis and tangent to y=x^2+4x-17 at (5/2,-3/4)

Answer 1

The equation of the curve is $y=x^2+4x-17$. Differentiating,

$\frac{dy}{dx}=2x+4$.

The slope of the tangent at $(5/2,-3/4)$ is

$m=2*\frac{5}{2} +4=9$. The angle the tangent makes with the x-axis is

$\theta$. Then,

$\tan \theta =9\\ \theta =\tan^{-1} 9=83.66^o$

The angle the tangent makes with the positive y-axis is

$90^o-\theta =90^o-83.66^o=6.34^o$