• # question_answer For the function$f(x)=\frac{4}{3}{{x}^{3}}-8{{x}^{2}}+16x+5x=2$is a point of A) local maxima    B) local minima C) point of inflection D) none of these

[c] : $f(x)=\frac{4}{3}{{x}^{3}}-8{{x}^{2}}+16x+5$                        ...(i) Differentiating (i) with respect to x, we get $f'(x)=\frac{4}{3}\times 3{{x}^{2}}-16x+16=4{{x}^{2}}-16x+16$ Now for maximum/minimum we put$f'(x)=0$ $\Rightarrow$${{x}^{2}}-4x+4=0\Rightarrow {{(x-2)}^{2}}=0\Rightarrow x=2$ $f''(x)=8x-16,f''(x){{|}_{at\,x=2}}=0$ $f'''(x)=8\ne 0$ $\therefore$ x = 2 is the point of inflection,