Statement - 1: Equation of tangents to the curve $y = f (x) = x^{2}$ at the point where slope of tangent is equal to functional value of the curve is $4 x - y - 4 = 0, y = 0$
Statement - 2: $f^{'} (x) = f (x)$

Question

Statement - 1: Equation of tangents to the curve $y = f (x) = x^{2}$ at the point where slope of tangent is equal to functional value of the curve is $4 x - y - 4 = 0, y = 0$

Statement - 2: $f^{'} (x) = f (x)$

TestHub · Accepted Answer

Given f ′ ( x ) = f ( x ) ⇒ 2 x = x 2 ⇒ x = 0 , 2 At x = 0 , y = 0 and at x = 2 , y = 4 So, we have to find equation of tangents at ( 0 , 0 ) and ( 2 , 4 ) At (0, 0), f ′ ( 0 ) = 0 ; at ( 2 , 4 ) , f ′ ( 2 ) = 4 ∴ tangents are y = 0 and 4 x − y − 4 = 0

Mathematics - Application of Derivative Question with Solution | TestHub

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