Iff'(x)=g(x) and g'(x)=-f(x) for all x and f(5)=2=f'(5). Then f2(10)+g2(10) is
8
16
32
64
Explanation for the correct option:
Step 1: Find the first derivative of [f(x)2+g(x)2]
Let us consider,
h(x)=[f(x)2+g(x)2]
Differentiating h(x) with respect to x we get,
h'(x)=2f(x)f'(x)+2g(x)g'(x)=2f(x)g(x)+2g(x)[-f(x)]=0
Step 2: Find the value of f2(10)+g2(10)
Finding h(10) we will get,
h'(x)=0⇒h(x)=constant⇒h(5)=h(10)
Now,
f2(5)+g2(5)=f2(5)+f'2(5)=22+22=8.
Hence, the correct option is A.