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Chapter 4: Problem 9
What two nonnegative real numbers with a sum of 23 have the largest possible product?
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Differentials Consider the following functions and express the relationship between a small change in \(x\) and the corresponding change in \(y\) in the form \(d y=f^{\prime}(x) d x\) $$f(x)=e^{2 x}$$
Linear approximation a. Write an equation of the line that represents the linear approximation to the following functions at a. b. Graph the function and the linear approximation at a. c. Use the linear approximation to estimate the given quantity. d. Compute the percent error in your approximation. $$f(x)=\tan x ; a=0 ; \tan 3^{\circ}$$
Given the following velocity functions of an object moving along a line, find the position function with the given initial position. Then graph both the velocity and position functions. $$v(t)=2 \cos t ; s(0)=0$$
Use analytical methods to evaluate the following limits. $$\lim _{x \rightarrow \infty} \frac{\log _{2} x}{\log _{3} x}$$
Give an argument to support the claim that if a function is concave up at a point, then the tangent line at that point lies below the curve near that point.
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