Statement - 1: A tangent parallel to x-axis can be drawn for $f (x) = (x - 1) (x - 2) (x - 3)$ in the interval [1, 3]

Statement - 2: A horizontal tangent cannot be drawn in [1, 3]

Question

Statement - 1: A tangent parallel to x-axis can be drawn for f ( x ) = ( x − 1 ) ( x − 2 ) ( x − 3 ) in the interval [1, 3] Statement - 2: A horizontal tangent cannot be drawn in [1, 3]

TestHub · Accepted Answer

Apply Rolle's Theorem: f is continuous on [1, 3], differentiable on ( 1 , 3 ) and f ( 1 ) = f ( 3 ) = 0 , so there exists c ∈ ( 1 , 3 ) with f ′ ( c ) = 0 ; a tangent parallel to the x-axis exists. Statement 1 is true and statement 2 is false.

Mathematics - Application of Derivative Question with Solution | TestHub

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