Question

1. - / 4.54 points find the first and second derivatives of the following function. f(x) = 2x⁴ - 6x³ + 4x f(x) = f(x) = resources read it watch it

Explanation:

Step1: Compute first derivative

Apply power rule: $\frac{d}{dx}(x^n)=nx^{n-1}$.
$f'(x)=2*4x^{3}-6*3x^{2}+4*1x^{0}=8x^3-18x^2+4$

Step2: Compute second derivative

Differentiate $f'(x)$ using power rule.
$f''(x)=8*3x^{2}-18*2x^{1}+0=24x^2-36x$

Answer:

$f'(x)=8x^3-18x^2+4$
$f''(x)=24x^2-36x$