First passage in a stochastic process may be influenced by the presence of an external confining potential, as well as "stochastic resetting" in which the process is repeatedly reset back to its initial position. Here, we study the interplay between these two strategies, for a diffusing particle in a one-dimensional trapping potential V(x), being randomly reset at a constant rate r. Stochastic resetting has been of great interest as it is known to provide an "optimal rate" (r_{*}) at which the mean first passage time is a minimum. On the other hand, an attractive potential also assists in the first capture process. Interestingly, we find that for a sufficiently strong external potential, the advantageous optimal resetting rate vanishes (i.e., r_{*}→0). We derive a condition for this optimal resetting rate vanishing transition, which is continuous. We study this problem for various functional forms of V(x), some analytically, and the rest numerically. We find that the optimal rate r_{*} vanishes with a deviation from the critical strength of the potential as a power law with an exponent β which appears to be universal.