Question

find f(0), f(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.
f(x)=3x^{5}-9x^{2}+8
what is f(0)?
f(0)=\square

Explanation:

Step1: Differentiate \( f(x) \)

Use the power rule \((x^n)^\prime = nx^{n - 1}\).
For \( f(x)=3x^{5}-9x^{2}+8 \), \( f^\prime(x)=3\times5x^{4}-9\times2x+0 = 15x^{4}-18x \).

Step2: Evaluate \( f^\prime(0) \)

Substitute \( x = 0 \) into \( f^\prime(x) \).
\( f^\prime(0)=15\times0^{4}-18\times0 = 0 \).

Answer:

\( 0 \)