Question

For the function f(x)=3 x⁴-4 x³-4 x²+2, find fʹ'(x). Then find fʹ'(0) and fʹ'(5).
fʹ(x)=

Answer 1

The derivative of the function f(x)=3 x⁴-4 x³-4 x²+2 is f'(x) = 12 x³ - 12 x² - 8 x. f'(0) = 0 and f'(5) = 260.

Step-by-step explanation:

The derivative of the function f(x)=3 x⁴-4 x³-4 x²+2 is f'(x) = 12 x³ - 12 x² - 8 x.

To find f'(0), substitute x=0 into the derivative. f'(0) = 12(0)³ - 12(0)² - 8(0) = 0.

To find f'(5), substitute x=5 into the derivative. f'(5) = 12(5)³ - 12(5)² - 8(5) = 600 - 300 - 40 = 260.