is 3.One possible equation of this line is y = 3x - 16.The line is tangent to the graph of y = f(x). The slope of the line is the same as the instantaneous rate of increase of f(x) at ![\begin{aligned}&\lim_{h\to 0}{\frac{f(3+h)-f(h)}{h}}\\ =&\lim_{h\to 0}\frac{1}{h} \cdot [(3^{3} + 3 \times 3^{2}h +3\times 3h^{2} + h^{3})- 4(3^{2} + 2\times 3h + h^{2}) + 2 \\[-1em] &\phantom{\lim_{h\to 0}\frac{1}{h}\cdot []} -(3^{3} -4\times 3^{2} + 2)]\\ = &\lim_{h \to 0}\frac{h^{3} + 5h^{2} +3h}{h}\\=& \lim_{h \to 0}{h^{2}} + \lim_{h \to 0}{5h} + \lim_{h\to 0}{3}\\ =& 3\end{aligned}](/tpl/images/0172/6928/2db87.png)
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Answer
1.consider the function f(x) = x^3 − 4x^2 + 2. calculate the limit of the difference qu...
Mathematics, 07.08.2019 10:10 calebcoolbeans6691
Answer
1.consider the function f(x) = x^3 − 4x^2 + 2. calculate the limit of the difference quotient at x0 = 3 for f(x).
2.find the equation of a line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit you found in part a.
3.graph the function f(x) and the line you identified in part b. how do the graphs relate to each other? what does the slope of the line represent about the function at the given point?
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