Question

In: Math

part 1) Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of...

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].

Expert Solution

#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

milcah answered 2 years ago

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