Consider the function below. f(x) = 5 + 2x2 − x4 (a) find the interval of increase. (enter your answer using interval notation.)

that is where the first dervitive is positive

take dervitive

find the zeroes and find the signs by plugging in values between

f'(x)=0, 0=4x-4x^3, 0=(4x)(1-x^2), 0=(4x)(1-x)(1+x), x=-1, 0, 1

by subsituting values for x in the ranges and seeing the signs of the factors we get

to the left of -1, f'(x) is positive

between -1 and 0, f'(x) is negative

between 0 and 1, f'(x) is positive

to the right of 1, f'(x) is negative

so it increasing to the left of -1 and in between 0 and 1

increasing on the interval (-∞,-1) U (0,1)