Optimization of a Nested Polynomial Function

00:00 4 marks

Consider the function $f(x) = (x^2 + 4x + 5)^3$.

(a) Find the x-coordinate at which $f(x)$ attains its minimum value using the first derivative test.

(b) Compute the minimum value of $f(x)$.

Hint Hint

Hint

Think about the relationship between the derivative of a function and its minimum values.

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Answer Answer

Complete Answer

a) x = -2; b) Minimum value = 1

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