Question

y = − 3 x 2 + 5 x − 8 Find the Maximum/Minimum value

Answer 1

Answer:

Given y=(x−2)6(x−3)5.     

Differentiating, we get 

dxdy=6(x−2)5(x−3)5+5(x−3)4(x−2)6

=(x−2)5(x−3)4(11x−28)

∴dxdy=(x−2)4(x−3)4.11(x−2)(x−1128)

For maxima or minima, 

dxdy=0

⇒x=2,3,1128

Now at x=2, dxdy changes from +ive to -ive. 

∴ Maximum is at x=2 and maximum value is 0.

At x=1128,dxdy changes from -ive to +ive ∴ minimum  at x=1128

∴ Minimum value of y=(