Question
If \(f(x)=\frac{3x^{2}-1}{4x+1}\) , then f′(−1)=
A \(-\frac{14}{3}\)
B \(-\frac{3}{2}\)
C \(\frac{14}{9}\)
D \(\frac{22}{9}\)
Answer/Explanation
Ans:C
This question involves the use of the quotient rule to calculate the derivative of a function at a specific point.
\(f'(x)=\frac{(4x+1)(6x)-(3x^{2}-2)(4)}{(4x+1)^{2}}=\frac{12x^{2}+6x+8}{(4x+1)^{2}}\)
Question
The graphs of the functions f and g are shown above. If h(x)=f(x)+1g(x)+3x, then h′(2)=
A \(\frac{1}{2}\)
B \(\frac{9}{100}\)
C \(\frac{1}{100}\)
D \(\frac{1}{10}\)
Answer/Explanation
Ans: C
Question
What is the slope of the line tangent to the graph of \(y=\frac{4x^{3}}{x+3}\) at x=1 ?
A 1
B \(\frac{11}{4}\)
C \(\frac{13}{4}\)
D 12
Answer/Explanation
Question
If \(f(x)=\frac{x-1}{x+1}\) for all x ≠ −1, then f ′(1) =
(A) –1 (B) \(−\frac{1}{2}\) (C) 0 (D) \(\frac{1}{2}\) (E) 1