Question: Let a,b,c,d be real numbers. Consider the function f(x) = ax^3 + bx^2 + cx + d a. Prove that this function can have at

Let a,b,c,dbe real numbers. Consider the function f(x) = ax^3 + bx^2 + cx + d

a. Prove that this function can have at most 2 extreme values.

b. State the condition on a, b and c such that it has exactly two extreme values.

c. Explain why d does not have a role in the location of the critical numbers.

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