Question

part 1)

Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of f and determine its inflection point(s).

part 2)

Find the absolute extrema of f(x) = x^4 + 4x^3 − 8x^2 + 3 on [−1, 2].

Answer 1

#1

Differentiating with respect to x

Again differentiating with respect to x

For inflection points

Infletion points are

Function f(x) is Concave up if f''(x)>0

Function is concave down if f''(x)<0

#2

Differentiating with respect to x

For critical points

In the interval

At boudary

So

Absolute minimum

Absolute maximum