Question

f(x)=4x³-x²+5.? And find each value

Answer 1

Answer:

Correct option is

D

25

Given, f(x)=4x3−x2−2x+1

Taking first derivative of the function f(x) we get

f′(x)=2(6x2−x−1)

Putting this equals to zero we get, x=−31, 21. 

Taking second derivative of f(x) we get, f′′(x)=2(12x−1) this shows that f(x) has a local maxima at x=−31 and a local minima at x=21. 

Which means in between 0≤x≤1 f(x) has a minima at 1/2 and f(x)=1 at x=0 and f(x)=2 at x=1, also f(x)=1/4 at x=1/2.

As per question we have g(x)= Min f(t):0≤t≤x,

g(41) = f(41) as min of f(x) in between 0 to 1/4 is at 1/4

f(41) = 1/2

g(43