


Ex 6.3
Ex 6.3,2
Ex 6.3,3 Important
Ex 6.3,4
Ex 6.3, 5 Important
Ex 6.3,6
Ex 6.3,7 Important
Ex 6.3,8
Ex 6.3,9 Important
Ex 6.3,10
Ex 6.3,11 Important
Ex 6.3,12
Ex 6.3,13
Ex 6.3, 14 (i)
Ex 6.3, 14 (ii) Important
Ex 6.3, 14 (iii)
Ex 6.3, 14 (iv) Important
Ex 6.3, 14 (v)
Ex 6.3,15 Important
Ex 6.3,16
Ex 6.3,17 You are here
Ex 6.3,18 Important
Ex 6.3,19
Ex 6.3,20
Ex 6.3,21 Important
Ex 6.3,22
Ex 6.3,23 Important
Ex 6.3,24 Important
Ex 6.3,25
Ex 6.3,26 (MCQ) Important
Ex 6.3,27 (MCQ)
Last updated at April 14, 2021 by Teachoo
Ex 6.3, 17 Find the points on the curve 𝑦=𝑥3 at which the slope of the tangent is equal to the y-coordinate of the pointLet the Point be (ℎ , 𝑘) on the Curve 𝑦=𝑥3 Where Slope of tangent at (ℎ , 𝑘)=𝑦−𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑓 (ℎ, 𝑘) i.e. 〖𝑑𝑦/𝑑𝑥│〗_((ℎ, 𝑘) )=𝑘 Given 𝑦=𝑥^3 Differentiating w.r.t.𝑥 𝑑𝑦/𝑑𝑥=3𝑥^2 ∴ Slope of tangent at (ℎ , 𝑘) is 〖𝑑𝑦/𝑑𝑥│〗_((ℎ, 𝑘) )=3ℎ^2 From (1) 〖𝑑𝑦/𝑑𝑥│〗_((ℎ, 𝑘) )=𝑘 3ℎ^2=𝑘 Also Point (ℎ , 𝑘) is on the Curve 𝑦=𝑥^3 Point (ℎ , 𝑘) must Satisfy the Equation of Curve i.e. 𝑘=ℎ^3 Now our equations are 3ℎ^2=𝑘 …(1) & 𝑘=ℎ^3 …(2) Putting Value of 𝑘=3ℎ^2 in (3) 3ℎ^2=ℎ^3 ℎ^3−3ℎ^2=0 ℎ^2 (ℎ−3)=0 ℎ^2=0 ℎ=0 ℎ−3=0 ℎ=3 When 𝒉=𝟎 3ℎ^2=𝑘 3(0)=𝑘 𝑘=0 Hence, point is (0, 0) When 𝒉=𝟑 3ℎ^2=𝑘 3(3)^2=𝑘 𝑘=27 Hence, point is (3 , 27)