The curve y(x)=a x³+b x²+c x+5 touches the x -axis at the point P(-2,0) and cuts the y -axis at the point Q, where y^() is equal to 3. Then the local maximum value of y(x) is:

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jul, Morning shift · Q2669

JEE Main 202225 Jul, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

The curve

y(x)=a x^{3}+b x^{2}+c x+5

touches the

x

-axis at the point

\mathrm{P}(-2,0)

and cuts the

y

-axis at the point

Q

, where

y^{\prime}

is equal to 3 . Then the local maximum value of

y(x)

is:

JEE Main 2022 · 25 Jul, Morning shift · Q2669

JEE Main 202225 Jul, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

The curve

y(x)=a x^{3}+b x^{2}+c x+5

touches the

x

-axis at the point

\mathrm{P}(-2,0)

and cuts the

y

-axis at the point

Q

, where

y^{\prime}

is equal to 3 . Then the local maximum value of

y(x)

is: