Question

On the curve y = x + =, find the points at which the tangents to the curve are parallel to the
x-axis.
х​

Answer 1

Answer:

Step-by-step explanation:

y=2x

3

−15x

2

+36x−21

dx

dy

​

=6x

2

−30x+36

Now,

dx

dy

​

=0

or, 6x

2

−30x+36=0

or, x

2

−5x+6=0

or, x

2

−3x−2x+6=0

or, x(x−3)−2(x−3)=0

x=2,x=3

when x=2

(y)

x=2

​

=2.2

3

−15.2

2

+36.2−21=16−60+72−21=7

(

dx

dy

​

)

x=2

​

=6.2

2

−30.2+36=24−60+36=0

(y)

x=3

​

=2.3

3

−15.3

2

+36.3−21=6

Points are (2,7),(3,6)

The equation of tangent at (2,7) parallel to x-axis y−7=0(x−2) y−7=0

The equation of tangent at (3,6) parallel to x-axis is y−6=0(x−3) or y−6=0.