Question

Help plz!!!
The following graph describes function 1, and the equation below it describes function 2:

Function 1: graph of function f of x equals negative x squared plus 8 multiplied by x minus 15

Function 2: f(x) = −x2 + 2x − 3
Function ______ has the larger maximum. (Put 1 or 2 in the blank space)

Answer 1

Answer with explanation:

→→→Function 1

f(x)= - x²+ 8 x -15

Differentiating once , to obtain Maximum or minimum of the function

f'(x)= - 2 x + 8

Put,f'(x)=0

-2 x+ 8=0

2 x=8

Dividing both sides by , 2, we get

x=4

Double differentiating the function

f"(x)= -2, which is negative.

Showing that function attains maximum at ,x=4.

Now,f(4)=-4²+ 8× 4-15

           = -16 +32 -15

          = -31 +32

          =1

→→→Function 2:

f(x) = −x² + 2 x − 3

Differentiating once , to obtain Maximum or minimum of the function

f'(x)= -2 x +2

Put,f'(x)=0

-2 x +2=0

2 x=2

Dividing both sides by , 2, we get

x=1

Double differentiating the function,gives

f"(x)= -2 ,which is negative.

Showing that function attains maximum at ,x=1.

f(1)= -1²+2 ×1 -3

   = -1 +2 -3

  = -4 +2

 = -2

⇒⇒⇒Function 1  has the larger maximum.