2. (The Cauchy-Schwarz Inequality for Integrals) Suppose that the functions f. g, f, g, and fg...

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2. (The Cauchy-Schwarz Inequality for Integrals) Suppose that the functions f. g, f², g², and fg are integrable on the closed, bounded interval [a, b]. Prove that 8 ≤ (Hint: For each numberà, define p() = ftf-àg]². Show that p(x) is a quadratic polynomial for which p(2) ≥ 0 for all and therefore that its discriminant is not positive.) 2. (The Cauchy-Schwarz Inequality for Integrals) Suppose that the functions f. g, f², g², and fg are integrable on the closed, bounded interval [a, b]. Prove that 8 ≤ (Hint: For each numberà, define p() = ftf-àg]². Show that p(x) is a quadratic polynomial for which p(2) ≥ 0 for all and therefore that its discriminant is not positive.)

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