Question

F(x)= x⁴−5x³. Find all critical values of f.

a) x=0,5
b) x=0,3
c) x=0,4
d) x=0,1

Answer 1

The critical values of the function f(x) are found by first taking the derivative f'(x) = 4x³ - 15x², setting it to zero, and then solving for x. The correct critical values are x = 0 and x = 3.75. None of the given options are correct.

Step-by-step explanation:

To find the critical values of f(x) = x⁴ - 5x³, we need to find the values of x where the derivative of f(x) is equal to 0 or undefined. The derivative of f(x) is f'(x) = 4x³ - 15x². Setting f'(x) equal to 0, we get 4x³ - 15x² = 0. Factoring out x², we have x²(4x - 15) = 0. So the critical values of f(x) are x = 0 and x = 15/4 = 3.75.