The tangent line to the graph f(x)=x^2+3x-18 at x=10 meets the x-axis at angle AOB?

Question

Angle AOB has a tangent of ________ and an angle measurement of ______ radians

Answer 1

m = 2x+3 = 23 at x = 10
angle = arctan(23) = 1.53 radians

I have assumed that angle AOB is the smaller of the two angles formed by the tangent line and the x-axis.

Answer 2

Find the value of the slope at the desired point

df/dx = 2x + 3

at x = 10 gives us m = 23

The tangent line will make the angle with the horizontal axis of

tan(theta) = m => theta = 87.51 degrees