To find f'(3) (f prime of 3), you must find f' first. f' is the derivative of the function f(x).
Finding the derivative of f(x) = 2x⁴ requires the use of the power rule.
The power rule for derivatives is [tex]\frac{d}{dx} [x^{n} ] =nx^{n-1}[/tex]. In other words, you bring the exponent forward and multiply it by the coefficient of the term, and then you subtract 1 from the original exponent.
f'(x) = [tex]\frac{d}{dx}[/tex](2x⁴)
f'(x) = 2(4)x³
f'(x) = 8x³
Now, to find f'(3), plug 3 into your derivative.
f'(3) = 8(3)³
f'(3) = 216
Answer:
f'(3) = 216
