Find the second derivative of $f ( x ) = \frac { 1 } { 3 } x ^ { 3 / 2 } - \frac { 4 } { 3 } x ^ { 1 / 4 } + 5 x - 2$
A) $\frac { 1 } { 4 }$ $x - 1 / 2$ + $\frac { 1 } { 4 }$ $x _ { } ^ { 7 / 4 }$
B) $\frac { 1 } { 4 }$ $x - 1 / 2$ - $\frac { 1 } { 4 }$ $x ^ { - 7 / 4 }$
C) $\frac { 2 } { 9 }$ $\times 1 / 2$ - $\frac { 16 } { 3 }$ $x - 3 / 4$ + 5
D) $\times 1 / 2$ + $\frac { 4 } { 9 }$ $x ^ { - 7 / 4 }$
E) $\frac { 1 } { 2 }$ $\times 1 / 2$ - $\frac { 1 } { 3 }$ $x - 3 / 4$ + 5

Question

Find the second derivative of $f ( x ) = \frac { 1 } { 3 } x ^ { 3 / 2 } - \frac { 4 } { 3 } x ^ { 1 / 4 } + 5 x - 2$
A) $\frac { 1 } { 4 }$ $x - 1 / 2$ + $\frac { 1 } { 4 }$ $x _ {  } ^ { 7 / 4 }$
B) $\frac { 1 } { 4 }$ $x - 1 / 2$ - $\frac { 1 } { 4 }$ $x ^ { - 7 / 4 }$
C) $\frac { 2 } { 9 }$ $\times 1 / 2$ - $\frac { 16 } { 3 }$ $x - 3 / 4$ + 5
D) $\times 1 / 2$ + $\frac { 4 } { 9 }$ $x ^ { - 7 / 4 }$
E) $\frac { 1 } { 2 }$ $\times 1 / 2$ - $\frac { 1 } { 3 }$ $x - 3 / 4$ + 5

Quizplus · Accepted Answer

To find the second derivative of $f(x) = \frac{1}{3}x^{3/2} - \frac{4}{3}x^{1/4} + 5x - 2$, we first find the first derivative and then differentiate it again. The first derivative is $f'(x) = \frac{1}{2}x^{1/2} - \frac{1}{3}x^{-3/4} + 5$. Differentiating this again gives $f''(x) = \frac{1}{4}x^{-1/2} + \frac{1}{4}x^{-7/4}$, which matches choice B after simplifying.

Find the Second Derivative Of f(x)=13x3/2−43x1/4+5x−2f ( x ) = \frac { 1 } { 3 } x ^ { 3 / 2 } - \frac { 4 } { 3 } x ^ { 1 / 4 } + 5 x - 2f(x)=31​x3/2−34​x1/4+5x−2

Find the Second Derivative Of $f ( x ) = \frac { 1 } { 3 } x ^ { 3 / 2 } - \frac { 4 } { 3 } x ^ { 1 / 4 } + 5 x - 2$