Question

the function f is a polynomial of degree 4. the derivative function of f has the following properties

Answer 1

\[f'(1)=0, f'(x)<0 for \left\{ X:X<1 \right\}\]
\[ f'(2)=0, f'(x)>0 for \left\{ x:1<x<2 \right\}\cup \left\{ x:x>2 \right\}\]

A. aminimum at x= 2 and a stationary point of inflection at x=1
B. a local minimum at x=2and a local maximum at x=1
C. a stationary point of inflection at x=2 and minimum at x=1
D. a stationary point of inflection at x=2 and mximum at x=1
E. a local maximum at x=2 ande a local minimum at x=1

Answer 2

Draw a little graph of it. You know that at points where f'(x) = 0, then the graph needs to be "horizontal" at that point? And where f'(x) > 0 it means that the graph is increasing (it's getting larger) and where f'(x) < 0, the graph is going smaller? That's enough to draw a picture and then you can easily see what's going on.