If the curve $y = a{x^3} + b{x^2} + cx$ is inclined at ${45^0}$ to $x$-axis at (0, 0) but touches $x$-axis at (1, 0), then

JEE MATHEMATICS MCQ: TANGENTS & NORMALS

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Application +4 | -1

If the curve

y = a{x^3} + b{x^2} + cx

is inclined at

{45^0}

x

-axis at (0, 0) but touches

x

-axis at (1, 0), then

View answer and explanation

Correct option: A

a = 1,\;b = - 2,\;c = 1

Option A (

a = 1,\;b = - 2,\;c = 1

) is correct because these values satisfy the given conditions of the curve's inclination and tangency.

Practice All Chapter MCQs →

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