Question

If g is the function given by g(x) = (1/3)x³ - (3/2)x² - 70x + 5, find all critical numbers.

a) x = -7
b) x = -5
c) x = 0
d) x = 7

Answer 1

The critical numbers of the function g(x) = (1/3)x³ - (3/2)x² - 70x + 5 are x = -7 and x = 10.

Step-by-step explanation:

The critical numbers of a function are the values of x where the derivative of the function is either zero or does not exist. To find the critical numbers of the function g(x) = (1/3)x³ - (3/2)x² - 70x + 5, we need to find the derivative of the function and set it equal to zero.

The derivative of g(x) is g'(x) = x² - 3x - 70.

Setting g'(x) equal to zero, we get x² - 3x - 70 = 0. This is a quadratic equation that can be factored as (x + 7)(x - 10) = 0. Therefore, the critical numbers of g(x) are x = -7 and x = 10.