Math, asked by nishitakumari040404, 4 months ago

The curve f(x)=x^3-3x^2-9x+9 has a point of inflexion at

Answers

Answered by roshangowda
0

Answer:

Set the second derivative equal to

0

then solve the equation

6

x

6

=

0

.

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x

=

1

Find the points where the second derivative is

0

.

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(

1

,

12

)

Split

(

,

)

into intervals around the points that could potentially be inflection points.

(

,

1

)

(

1

,

)

Substitute a value from the interval

(

,

1

)

into the second derivative to determine if it is increasing or decreasing.

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Decreasing on

(

,

1

)

since

f

''

(

x

)

<

0

Substitute a value from the interval

(

1

,

)

into the second derivative to determine if it is increasing or decreasing.

Tap for more steps...

Increasing on

(

1

,

)

since

f

''

(

x

)

>

0

An inflection point is a point on a curve at which the concavity changes sign from plus to minus or from minus to plus. The inflection point in this case is

(

1

,

12

)

.

(

1

,

12

)

image of graph

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