Question

for what value of x does f(x)=x3−x reach its maximum, constrained to the set x<0? give your answer to 2 significant digits.

Answer 1

Below in bold.

Explanation:

f(x) = x^3 - x

Finding the derivative:

f'(x) = 3x^2 - 1

At a maximum/minimum

3x^2 - 1 = 0

x^2 = 1/3

x = +/- √(1/3) or +/- 0.57735

As x < 0 the answer is -0.58 to 2 s.f's.

This gives a maximum value of f(x) as the second derivative 6x with x = -0.58 gives a negative value.