Question

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

Answer 1

that is where the first dervitive is positive

take dervitive

`f'(x)=4x-4x^3`

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)