For a cubic \( f(x)=\frac{a x^{3}}{3}+(a+2) x^{2}+(a-1) x+2 \) find 'a' if \( f(x) \) have (a) '+ve' pt of local max. (b) '-ve' pt of local minima (c) '+ve' pt. of inflexion (d) No extrema. (e) 3-repeated roots.

Question

For a cubic \( f(x)=\frac{a x^{3}}{3}+(a+2) x^{2}+(a-1) x+2 \) find 'a' if \( f(x) \) have (a) '+ve' pt of local max. (b) '-ve' pt of local minima (c) '+ve' pt. of inflexion (d) No extrema. (e) 3-repeated roots.