We present [C/N]–[Fe/H] abundance trends from the SDSS-IV Apache Point Observatory Galactic Evolution Experiment survey, Data Release 14 (DR14), for red giant branch stars across the Milky Way (3 kpc < R < 15 kpc). The carbon-to-nitrogen ratio (often expressed as [C/N]) can indicate the mass of a red giant star, from which an age can be inferred. Using masses and ages derived by Martig et al., we demonstrate that we are able to interpret the DR14 [C/N]–[Fe/H] abundance distributions as trends in age–[Fe/H] space. Our results show that an anticorrelation between age and metallicity, which is predicted by simple chemical evolution models, is not present at any Galactic zone. Stars far from the plane (| Z| > 1 kpc) exhibit a radial gradient in [C/N] (∼‑0.04 dex kpc‑1). The [C/N] dispersion increases toward the plane (σ [C/N] = 0.13 at | Z| > 1 kpc to σ [C/N] = 0.18 dex at ∣Z∣ < 0.5 kpc). We measure a disk metallicity gradient for the youngest stars (age < 2.5 Gyr) of ‑0.060 dex kpc‑1 from 6 to 12 kpc, which is in agreement with the gradient found using young CoRoGEE stars by Anders et al. Older stars exhibit a flatter gradient (‑0.016 dex kpc‑1), which is predicted by simulations in which stars migrate from their birth radii. We also find that radial migration is a plausible explanation for the observed upturn of the [C/N]–[Fe/H] abundance trends in the outer Galaxy, where the metal-rich stars are relatively enhanced in [C/N].