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Question 14 (OR 2nd Question) - CBSE Class 12 Sample Paper for 2020 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

For the curve  y = 5x − 2x 3 , if x increases at the rate of 2 units/sec, then at x = 3 the slope of the curve is changing at _________

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Question 14 (OR 2nd Question) For the curve y = 5x − 2x3, if x increases at the rate of 2 units/sec, then at x = 3 the slope of the curve is changing at _________ Given y = 5x − 2x3 𝑑𝑥/𝑑𝑡 = 2 units/sec We need to find how fast the slope is changing We know that Slope = 𝑑𝑦/𝑑𝑥 = (𝑑(5𝑥 − 2𝑥^3))/𝑑𝑥 = 5 – 6x2 How was slope is changing is (𝑑(𝑆𝑙𝑜𝑝𝑒))/𝑑𝑡 Finding it (𝑑(𝑆𝑙𝑜𝑝𝑒))/𝑑𝑡 = (𝑑(5 − 6𝑥^2))/𝑑𝑡 = 0 – 12x 𝑑𝑥/𝑑𝑡 = –12x 𝑑𝑥/𝑑𝑡 Putting x = 3 and 𝑑𝑥/𝑑𝑡 = 2 units/sec = –12 × 3 × 2 = –72 So, Slope is decreasing at the rate of 72 units/sec
  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

    3. CBSE Class 12 Sample Paper for 2020 Boards

    CBSE Class 12 Sample Paper for 2019 Boards →
CBSE Class 12 Sample Paper for 2019 Boards →
Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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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 and Computer Science at Teachoo