Question

If f(x) = 2x^4, then f'(3) =

Answer 1

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 $\frac{d}{dx} [x^{n} ] =nx^{n-1}$.  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) = $\frac{d}{dx}$(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