Question

The maximum value of 7 + 6x – 9x2 is​

Answer 1

answer

The maximum value of y is 8.

We need to find the maximum value of the following expression :

y=7+6x-9x^2y=7+6x−9x

2

....(1)

For maximum value put \dfrac{dy}{dx}=0

dx

dy

=0

So,

\begin{gathered}\dfrac{d}{dx}(7+6x-9x^2)=0\\\\6-18x=0\\x=\dfrac{1}{3}\\\end{gathered}

dx

d

(7+6x−9x

2

)=0

6−18x=0

x=

3

1

Put x = 1/3 in equation (1) :

\begin{gathered}y=7+6\times \dfrac{1}{3}-9\times (\dfrac{1}{3})^2\\\\y=8\end{gathered}

y=7+6×

3

1

−9×(

3

1

)

2

y=8

So, the maximum value of y is 8.

Explanation:

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