For the function f(x) = 4x - x^2 find:?

Question

A. The coordinates of the vertex
B. The equation of the axis of symmetry
C. The greatest value of the function
D. The x and y coordinates to graph on a coordinate plane

Answer 1

you need to differentiate

f'(x)=4-2x

find when the gradient is 0
0=4-2x
x=2

put 2 in the original function to find y

y=4*2-2^2 = 2 so the vertex is 2, 2

the equation of the axis of symmetry is perpendicular to the f'(x) and goes through 2, 2
so g(x) will be g(x)=x/2+c

and we know that when g(x)=2, x=2, so
2=2/2+c
therefore c=1
g(x)=(x/2) -1

the greatest value of the function is 2 (which is y)

the x,y coordinated will be (2,2)

hope it helps

Answer 2

Part a)
f `(x) = 4 - 2x
4 - 2x = 0 for turning point
x = 2 for turning point
f " (x) = - 2
f(2) = 8 - 4 = 4
(2,4) is a MAX. turning point

Part b)
Axis of symmetry is x = 2

Part c)
Greatest value is f(x) = 4

Part d)
Some points are (0 , 0) , (2 , 4) , (4 , 0)