Question

Facorize: x⁴⁹y – x ⁵⁰y​

Answer 1

Answer:

x⁴⁹y (1 - x)

Step-by-step explanation:

x⁴⁹y – x ⁵⁰y​

• Taking y common

=> y(x⁴⁹ - x⁵⁰)

• Taking x⁴⁹ common

=> y x⁴⁹(1 - x)

=> x⁴⁹y (1 - x)

                                   

Hope this helps!

Answer 2

Answer:

f(x)=x

50

−x

20

in interval [0,1]

f

′

(x)=50x

49

−20x

19

(for critical points)

f

′

(x)=0

50x

49

=20x

19

x

30

=

5

2

x=±(

5

2

)

1/30

Now, maximum value f

⎣

⎢

⎡

(

5

2

)

1/30

⎦

⎥

⎤

=(

5

2

)

5/3

−(

5

2

)

2/3

=(

5

2

)

2/3

⎣

⎢

⎡

(

5

2

)

3

−1

⎦

⎥

⎤

=−

125

117

(

5

2

)

2/3

Minimum value, f

⎣

⎢

⎡

−(

5

2

)

1/30

⎦

⎥

⎤

=−(

5

2

)

5/3

+(

5

2

)

2/3

=(

5

2

)

2/3

⎣

⎢

⎡

(

5

2

)

3

−1

⎦

⎥

⎤

=−

125

133

(

5

2

)

2/3