Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematics Differential Calculus Applications of Derivatives
Let g : R → R be a non constant twice differentiable such that \(\mathrm{g}^{\prime}\left(\frac{1}{2}\right)=\mathrm{g}^{\prime}\left(\frac{3}{2}\right)\). If a real valued function f is defined as \(\mathrm{f}(\mathrm{x})=\frac{1}{2}[\mathrm{~g}(\mathrm{x})+\mathrm{g}(2-\mathrm{x})]\), then
1
f" (x) = 0 for atleast two x in (0, 2)
2
f" (x) = 0 for exactly one x in (0, 1)
3
f" (x) = 0 for no x in (0,1)
4
\(f^{\prime}\left(\frac{3}{2}\right)+f^{\prime}\left(\frac{1}{2}\right)=1\)