(Solved): Find the critical points of each of the following and classify them as relative max, relative min ...

Find the critical points of each of the following and classify them as relative max, relative min or neither using an appropriate test. Find all inflection points. a.) \( y=x^{3}-6 x+2 \) b.) \( y=(2 x-3)^{4 / 5} \) c.) \( y=x^{3}-6 x^{2}+12 x-8 \) Find the absolute maximum and absolute minimum of \( y=(2 x-3)^{4 / 5} \) on the interval \( [-1,2] \) Find the equations of any vertical asymptotes, horizontal asymptotes or slant asymptotes. Find all critical points. Find where the function is increasing or decreasing. Find coordinates of all relative maximum or minimums. a.) \( y=\frac{3 x-7}{2 x+5} \) b.) \( y=\frac{x^{2}-9}{x^{2}-1} \) c.) \( y=\frac{x^{2}+9}{x} \) Find the specific solution to a.) \( \frac{d y}{d x}=x^{2 / 3}+x+1 \) with \( y(0)=12 \) b.) \( \frac{d y}{d x}=x^{4}+1 \) with \( y(1)=2 \)