Let the function f:(0,π)→R be defined by f(θ)=(sinθ+cosθ)2+(sinθ−cosθ)4. Suppose the function f has a local minimum at θ precisely when θ∈{λ1π,…,λrπ}, where 0<λ1<⋯<λr<1. Then the value of λ1+⋯+λr is

Let the function f:(0,π)→R be defined by f(θ)=(sinθ+cosθ)2+(sin�

1.	Let the function f:(0,π)→R be defined by f(θ)=(sinθ+cosθ)2+(sinθ−cosθ)4. Suppose the function f has a local minimum at θ precisely when θ∈{λ1π,…,λrπ}, where 0<λ1<⋯<λr<1. Then the value of λ1+⋯+λr is
Answer» Let the function $f : (0, π) \to R$ be defined by $f (θ) = (sin θ + cos θ)^{2} + (sin θ - cos θ)^{4} .$ Suppose the function $f$ has a local minimum at $θ$ precisely when $θ \in {λ_{1} π, \dots, λ_{r} π},$ where $0 < λ_{1} < \dots < λ_{r} < 1.$ Then the value of $λ_{1} + \dots + λ_{r}$ is