If $f(t)=\sqrt{9 t+1}$ , find $f^{\prime \prime}(4)$ .
A) $-0.010$
B) $0.015$
C) $-0.033$
D) $-0.22$
E) $0.044$

Name: If $f(t)=\sqrt{9 t+1}$ , find $f^{\prime \prime}(4)$ . A) $-0.010$ B) $0.015$ C) $-0.033$ D) $-0.22$ E) $0.044$
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Quizplus · Accepted Answer

Using the chain rule, we have $f'(t)=\frac{1}{2\sqrt{9t+1}}\cdot 9=\frac{9}{2\sqrt{9t+1}}$ and $f''(t)=-\frac{9}{4(9t+1)^{3/2}}$. Therefore, $f''(4)=-\frac{9}{4(9(4)+1)^{3/2}}=-\frac{9}{4(37)^{3/2}}=-\frac{9}{4(37\sqrt{37})}=-\frac{9}{4(136.47)}=-0.010$.

If f(t)=9t+1f(t)=\sqrt{9 t+1}f(t)=9t+1​ , Find f′′(4)f^{\prime \prime}(4)f′′(4) A) −0.010-0.010−0.010 B) 0.0150.0150.015 C) −0.033-0.033−0.033 D) −0.22-0.22−0.22

If $f(t)=\sqrt{9 t+1}$ , Find $f^{\prime \prime}(4)$
A) $-0.010$ B) $0.015$ C) $-0.033$ D) $-0.22$