Question 22

If f(x) = $$x^3 - 4x + p$$ and f(0) and f(1) are of opposite signs, Which one of the following is neccessarily true?

Solution

Given f(x) = $$x^3 - 4x + p$$ and f(0) and f(1) are of opposite signs.

$$\Rightarrow f(0)\times f(1) < 0$$

$$f(0) = 0^3 - 4*0 + p = p$$

$$f(1) = 1^3 - 4*1 + p = p-3$$

$$\Rightarrow (p)(p-3) < 0$$

$$\Rightarrow 0 < p < 3$$.

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