A real number M is squared to give the value N. Find the minimum value of (M+N). Formula used: N=M2 Minimize(M+N)=M+M2 Calculation: Let f(M)=M+M2 To find the minimum value, take the derivative and set it to zero: f′(M)=1+2M ⇒1+2M=0 ⇒M=−0.5 Substitute M=−0.5 into f(M) : f(M)=M+M2 ⇒f(−0.5)=(−0.5)+(−0.5)2 ⇒f(−0.5)=−0.5+0.25 ⇒f(−0.5)=−0.25 ∴ The minimum value of (M+N) is −0.25, and the correct answer is option 1.
