Given:
A function
[tex]f(x)=-2x^2+9[/tex]
and value of g(x) at x.
To find:
Maximum value of both functions.
Explanation:
For criticle points find f'(x) = 0 and f''(x)>0. Then value will be maximum.
Solution:
Now, first derivative is
[tex]\begin{gathered} f^(x)=-2x^2+9 \\ f^{\prime}(x)=-4x \end{gathered}[/tex]
Now, put f'(x)=0 and criticle point will be 0.
Now,
[tex]f^{^^{\prime}^{\prime}}(x)=-4[/tex]
As second derivative of function is negetive at x=0. So, we will get maximum at x=0
So, At x=0
[tex]f(0)=9[/tex]
So, maximum value of f(x) is 9 and maximum value of g(x) is 11.
Hence, this is the maximum values of f(x) and g(x).
