Answer
${x = -5, 1}$
Work Step by Step
Original equation: ${f(x) = x^{3} + 6x^{2} - 15x}$
The critical numbers of a function are found when the derivative of a function is set to 0.
Finding the derivative of the function using the power rule:
${f'(x) = 3x^{2} + 12x - 15}$
Setting the derivative to equal 0:
${f'(x) = 3x^{2} + 12x - 15 = 0}$
Factoring out the 3:
${3x^{2} + 12x - 15 = 0}$
${3(x^{2} + 4x - 5) = 0}$
Solving the quadratic equation through factoring:
${3(x^{2} + 4x - 5) = 0}$
${3(x+5)(x-1) = 0}$
Solve for x:
${x = -5, 1}$
