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Chapter 3: Problem 39

Multiple Choice Let \(f(x)=4-3 x .\) Which of the following is equal to \(f^{\prime}(-1) ? \)(\mathbf{A})-6 \quad(\mathbf{B})-5 \quad(\mathbf{C}) 5 \quad(\mathbf{D}) 6 \quad(\mathbf{E})$ does not exist

Short Answer

Expert verified
The derivative \(f'(-1) = -3 \) is not in the multiple choices. Thus, there might be a mistake in the options provided.

Step by step solution

01

Differentiation

First, differentiate the function \(f(x)=4-3x\). The constant 4 becomes 0 when differentiated and -3x becomes -3. Hence, the derivative of the function, \(f'(x)\), is -3.
02

Substitution of x

Now substitute x = -1 into the derivative of the function: \(f'(-1) = -3\).

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Most popular questions from this chapter

Multiple Choice Which of the following is \(d y / d x\) if \(y=\cos ^{2}\left(x^{3}+x^{2}\right) ?\) (A) \(-2\left(3 x^{2}+2 x\right)\) (B) \(-\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)\) (C) \(-2\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)\) (D) 2\(\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)\) (E) 2\(\left(3 x^{2}+2 x\right)\)

In Exercises 61 and \(62,\) use the curve \(x^{2}-x y+y^{2}=1\) Multiple Choice Which of the following is equal to \(d y / d x ?\) (A) \(\frac{y-2 x}{2 y-x} \quad\) (B) \(\frac{y+2 x}{2 y-x}\) (C) \(\frac{2 x}{x-2 y} \quad\) (D) \(\frac{2 x+y}{x-2 y}\) \((\mathbf{E}) \frac{y+2 x}{x}\)

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The Derivative of \(\cos \left(x^{2}\right)\) Graph \(y=-2 x \sin \left(x^{2}\right)\) for \(-2 \leq x \leq 3 .\) Then, on screen, graph $$y=\frac{\cos \left[(x+h)^{2}\right]-\cos \left(x^{2}\right)}{h}$$ for \(h=1.0,0.7,\) and \(0.3 .\) Experiment with other values of \(h .\) What do you see happening as \(h \rightarrow 0 ?\) Explain this behavior.
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