Calculus Problem # 16

Solution: y-intercept: 0, x-intercept: 0, vertical asymptote at 1

Differentiating the function, we get:

That means that the function is increasing on and decreasing on. The critical points are 0 (local maximum) and 2 (local minimum). We differentiate again to get:

That implies that the function is concave up on and concave down on. The inflection points are and


Calculus Problem # 15

Find an equation of the line tangent to the curve y=x3 + (12/x) at
the point (2,5)
Solution: First of all, we need to differentiate the function. We find that
Now, in order to find the slope of the tangent line, we evaluate at, which yields
The equation of the tangent line is