Mathematics

Problem

Examine the function

y = (1 + 3x)^4

. a. (i) Compute

\dfrac{dy}{dx}

and

\dfrac{d^2y}{dx^2}

. b. (ii) Using the sign of

\dfrac{d^2y}{dx^2}

, explain why the graph of the function is concave upward for all real values of

x

. c. (iii) Describe how the result in part (ii) relates to the general behaviour of polynomial curves of even degree with positive leading coefficients.

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