Given:
Function 1 is given in the graph.
Function 2 is,
[tex]f(x)=-x^2+2x-15[/tex]
To find:
The function has a larger maximum value.
Explanation:
From the graph,
We know that the maximum value of the function is the highest point of the function.
For the function 1, the maximum value is 1 at x = 4.
For the function 2,
Differentiating with respect to x, we get
[tex]f^{\prime}(x)=-2x+2[/tex]
Equate it with zero, and we get
[tex]\begin{gathered} -2x+2=0 \\ x=1 \end{gathered}[/tex]
Substituting x = 1 in function 2.
[tex]\begin{gathered} f(1)=-1^2+2(1)-15 \\ =-14 \end{gathered}[/tex]
So, the maximum value is -14 at x = 1.
Then, comparing functions 1 and 2 we get,
Function 1 has the larger maximum value at (4, 1).
Final answer:
Function 1 has the larger maximum value at (4, 1).
