Question
Let g be the function given by \(g(x)=x^{4}-2x^{3}-3x\) . What are all values of x such that g′(x)=\(\frac{1}{2}\) ?
A −4.00
B 1.746
C 1.777
D −0.164 and 2.508
Answer/Explanation
Ans:C
Question
Let f be the function given by \(f(x)=2x^{3}+x^{2}-3\). What is the value of f′(2) ?
A 56
B 28
C 25
D 10
Answer/Explanation
Ans:B
Question
If \(f(x)=5x^{6}-3x^{5}+2x^{3}+x^{2}+e^{3}\), then f′(x)=
A \(5x^{5}-3x^{4}+2x^{2}-x\)
B \(30x^{5}-15x^{4}+6x^{2}-2x\)
C \(30x^{5}-15x^{4}+6x^{2}-2x+3e^{2}\)
D \(30x^{6}-15x^{5}+6x^{3}-2x^{2}\)
Answer/Explanation
Ans:B
This question involves using the power rule \(\frac{\mathrm{d} }{\mathrm{d} x}x^{n}=nx^{n-1}\) for differentiation of polynomial functions as follows.
\(6.5x^{5}-5.3x^{4}+3.2x^{2}-2x^{1}\)