Question

if x is real, then the maximum value 4+3x-x^2 will be equal to


please help me out ​

Answer 1

Answer:

To find stationary points, differentiate and set the differential to zero.

In this case, y=5+20x−4x2 . When we differentiating, terms without an x ‘disappear’ and terms with an xn ‘change’ to nxn^−1

Therefore, dy/dx=20−8x .

Setting this equal to zero, 20−8x=0

8x=20

x=20/8=5/2 .

Subbing this value back into the function, y=5+(20⋅5/2)−(4⋅(5/2)2)

y=5+50−25

y=30

Therefore the maximum point is at (5/2,30)