Question

y=x4-2x2+2find the horizontal tangent to the point​

Answer 1

Answer:

y

=

7

x

−

5

Explanation:

We have;

y

=

x

4

+

2

x

2

−

x

First we differentiate wrt

x

;

y

=

x

4

+

2

x

2

−

x

∴

d

y

d

x

=

4

x

3

+

4

x

−

1

We now find the vale of the derivative at

(

1

,

2

)

(and it always worth a quick check to see that

y

=

2

when

x

=

1

) we have

d

y

d

x

=

4

+

4

−

1

=

7

So at the tangent passes through the coordinate

(

1

,

2

)

and has gradient

m

=

7

We now use

y

−

y

1

=

m

(

x

−

x

1

)

to get the equation of the tangent:

∴

y

−

2

=

7

(

x

−

1

)

∴

y

−

2

=

7

x

−

7

∴

y

=

7

x

−

5