Use calculus to find the set of values of x for which f(x) = x^3 - 9x is an increasing function.
f(x) is an increasing function when its gradient is positive. To find the the gradient of the the function we must differentiate it:d/dx f(x) = 3x2 - 9. To differentiate we multiply the exponent by the coefficient, then subtract one from the exponent, we repeat this for each term in the function.The second part of this problem is finding when this gradient is positive: i.e. when 3x2 - 9 > 0. This can be rearranged to 3x2 > 9; then x2 > 3. Which is true for any |x| > sqrt(3). Therefore x > sqrt(3) and x < -sqrt(3)
