Let f be a twice differentiable function such that g'x=-fx and f'x=gx, hx=fx2+gx2. If h5=11, then h10 is equal to A. 22 B. 11 C. 0 D. 20

Question

Let f be a twice differentiable function such that g&#039;x=-fx and f&#039;x=gx, hx=fx2+gx2. If h5=11, then h10 is equal to A. 22 B. 11 C. 0 D. 20

Gabriel Valencia · Accepted Answer

Identify the value of h10.Consider the given equation as: hx=fx2+gx2Then, h&#039;x=2fx.f&#039;x+2gx.g&#039;x......(1)From the given datagx=f&#039;xg&#039;x=f&#039;&#039;xf&#039;&#039;x=-fxReplace the aforementioned values in the equation.(1)h&#039;x=2fx.f&#039;x-2gx.fxh&#039;x=2fx.gx-2gx.fxh&#039;x=0Since, hx has some constant value.Then, the value of h10 is given as:h10=h5=11h10=11Therefore, The correct answer is Option B

Let f be a twice differentiable function such that g'x=-fx and f'x=gx, hx=fx2+gx2. If h5=11,...

Answered question

Answer & Explanation