Let D2 be the operation of taking the second derivative. Find the image of 2x^2+3x^2-5x+4 under D2. Prove that D2 is a linear operator on Pn. Determing the kernel and range of D2.
D2=10......now where?
D is linear operator,since
D(f+g)=D(f)+D(g) and D(kf)=kD(f) for any $\displaystyle f,g \in P_n, k \in R$.
D(f)=0 if and only if $\displaystyle f \in P_2$.
D(Pn)=$\displaystyle P_{n-2}$ if n is greater than 2.