Question
If \(f(x)=x^{6}\), then f′(x)=
A \(x^{5}\)
B \(5x^{5}\)
C \(6x^{5}\)
D \(6x^{6}\)
Answer/Explanation
Ans:C
Question
If \(f(x)=\frac{1}{x^{6}}\), then f′(x)=
A \(\frac{1}{6x^{5}}\)
B \(-\frac{6}{x^{5}}\)
C \(-\frac{1}{6x^{7}}\)
D \(-\frac{6}{x^{7}}\)
Answer/Explanation
Ans:D
Question
If f is the function defined by \(f(x)=\sqrt[3]{x}\),what is f′(x) ?
A \(\frac{1}{3}x^{\frac{1}{3}}\)
B \(x^{-\frac{2}{3}}\)
C \(\frac{1}{3}x^{-\frac{2}{3}}\)
D \(3.\sqrt{x}\)
Answer/Explanation
Ans:C
\(f(x)=\sqrt[3]{x}=x^{\frac{1}{3}}\) is a power function. Therefore, the power rule is applied to determine the derivative.
Question
For what non-negative value of b is the line given by \(y=-\frac{1}{3}x+b\) normal to the curve \(y=x^{3}\)?
(A) 0 (B) 1 (C) \(\frac{4}{3}\) (D)\( \frac{10}{3}\) (E) \(\frac{10\sqrt{3}}{3}\)