Answer to Question #314386 in Real Analysis for Pankaj

Question

Determine the local minimum and local maximum values of the function f defined by

f(x) = 3-5x³ +5x⁴ -x^5

Answer 1

$f'\left( x \right) =-15x^2+20x^3-5x^4=-5x^2\left( x-1 \right) \left( x-3 \right) \\f'\left( x \right) =0\Rightarrow x\in \left\{ 0,1,3 \right\}$

Then we see that x=1 is local minimum, x=3 is local maximum