The given polynomial is,
![y=x^4-17x^2+16](https://img.qammunity.org/2023/formulas/mathematics/college/liwqptw4q2e6wjdzh7ubzzvtv29l8zu71b.png)
The graph of the function can be drawn as,
From the graph it is evident that the biquadratic equation has 4 real roots with 2 local minimas and 1 local maxima.
Thus, 1 local maximum and 2 local minimum is the correct options.