JEE MATHEMATICS MCQ: TANGENTS & NORMALS

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Analyzing +4 | -1

If the tangent at each point of the curve

y=\frac{2}{3} x^3-2 a x^2+2 x+5

makes an acute angle with the positive direction of

x

-axis, then

View answer and explanation

Correct option: B

-1 \leq a \leq 1

Option B (

-1 \leq a \leq 1

) is correct because the derivative of the curve must be non-negative for all x, leading to the given range for 'a'.

More Questions from TANGENTS & NORMALS

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a

y=x^3-a x

x^2 y=1-y

x y=1-y

C

y^3-3 x y+2=0

H

\mathrm{C}

x

V

C

y

y-e^{x y}+x=0

y = f\left( x \right)

x

x = a\left( {\theta - \sin \theta } \right),\;y = a\left( {1 + \cos \theta } \right)

\theta = \left( {2k + 1} \right)\pi ,\;k \in Z