Question

Let f(x)= x^4 + ax^2 +b. The graph of f has a relative minimum at (0,1) and an inflection point when x=1. The values of a and b are...

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Answer 1

`f(x)=x^4+ax^2+b\\f'(x)=4x^3+2ax\\f''(x)=12x^2+2a\\f''(1)=12(1)^2+2a\\12(1)=-2a\\a=-6\\\\f(x)=x^4-6x^2+b\\(1)=(0)^4-6(0)^2+b\\b=1`

a=-6
b=1