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Question 36 (ii) Find 𝑑𝑉/𝑑𝑥Now, V = 2(2𝑥^3−65𝑥^2+500𝑥) Diff w.r.t 𝑥 V’(𝑥)=2𝑑[2𝑥^3 − 65𝑥^2 + 500𝑥]/𝑑𝑥 = 2[6𝑥^2−65 × 2𝑥+500] = 2[6𝑥^2−130𝑥+500] = 2 × 2[3𝑥^2−65𝑥+250] = 4[𝟑𝒙^𝟐−𝟔𝟓𝒙+𝟐𝟓𝟎] Splitting the middle term Splitting the middle term method We need to find two numbers whose Sum = –65 Product = 3 × 250 = 750 = 4[3𝑥^2−50𝑥−15𝑥+250] = 4[𝑥(3𝑥−50)−5(3𝑥−50)] = 4[(𝑥−5)(3𝑥−50)] = 4(𝒙−𝟓)(𝟑𝒙−𝟓𝟎)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.