If f^ (0)=k , then _ x 0 2 f(x)-3 f(2 x)+f(4 x) x^2 is equal to

Step-by-step solution

aligned f^ (0) & =k and & _ x 0 2 f(x)-3 f(2 x)+f(4 x) x^2 aligned Using L'Hospital's rule, = _ x 0 2 f^ (x)-6 f^ (2 x)+4 f^ (4 x) 2 x Again, using L'Hospital's rule, aligned & = _ x 0 2 f^ (x)-12 f^ (2 x)+16 f^ (4 x) 2 & = 1 2 [2 f^ (0)-12 f^ (0)+16 f^ (0) ] & = 1 2 [2 k-12 k+16 k]=3 k aligned