The maximum value of f(x)=−3x2+5x+2 ∀ x∈[0,2] is
14736
f(x)=−3x2+5x+2
Here a<0⇒ graph is inverted cup shaped & maximum value will occur at x=−b2a=56
As 0<56<2
⇒ No other value of x in [0,2] will have
f(x)>f(56)
So, f(56) is the maximum value.
f(56)=−3x(56)2+5(56)+2 =14736