Linear algebra orthonormal basis?

Question

Assume that A ∈ M^n×n(R) admits an orthonormal basis of eigenvectors with eigenvalues λ₁ ≤ λ₂ ≤ · · · ≤ λ_n.

Show that λ₁∥v∥² ≤ Av · v ≤ λ_n∥v∥² for each v ∈ Rⁿ

So far I've got:

⟨v_i,v_j⟩ = 0 for i= ̸=j for an orthonormal basis

but I'm not sure about where to go from there

Any help will be appreciated! Thanks