InterviewSolution
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InterviewSolution
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Using Lagrange's Mean Value theorem , find the co-ordinates of a point on the curve y = x^(2) at which the tangent drawn is parallel to the line joining the points (1,1) and (3,9). |
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Answer» Solution :LET f(x) = `x^(2)` . Here given INTERVAL is [1,3]. (i) The function f(x) has definite and unique value in [1,3] `therefore` f(x) is continuous in [1,3] . (ii) f'(x) = 2x Which is defined in ]1,3[. `therefore` f(x) is differentiable in ]1,3[ . Thus the conditions of lagrange's Mean Value THEOREM satisfies . Now there exists at least one value of `c in ]1,3[` such that `f'(c) = (f(3) - f(1))/(3-1)` `implies "" 2C = (9-1)/(2) = 4` `implies "" c = 2 in ]1 , 3[` Hence Lagrange's Mean Value theorem verified . `therefore "" f(c) = c^(2)` `implies "" f(2) = 2^(2) = 4` `therefore "" ` The required point = (2,4). `""` Ans. |
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