
Slope of a Tangent Line Sketch the graph of the function
(a) Find the slope of the line joining (4, 2) and (9, 3). Is the slope of the tangent line at (4, 2) greater than or less than this number?
(b) Find the slope of the line joining (4, 2) and (1, 1). Is the slope of the tangent line at (4, 2) greater than or less than this number?
(c) Find the slope of the line joining (4, 2) and (4.41, 2.1). Is the slope of the tangent line at (4, 2) greater than or less than this number?
(d) Find the slope of the line joining (4, 2) and (4 + h, f(4+h)) in terms of the nonzero number h.
(e) What is the slope of the tangent line at (4, 2)? Explain how you arrived at your answer.

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Chapter P Solutions
Calculus
- Explain the relationship between 12.3.6, (case A of 12.3.6) and 12.3.7arrow_forwardExplain the key points and reasons for the establishment of 12.3.2(integral Test)arrow_forwardUse 12.4.2 to determine whether the infinite series on the right side of equation 12.6.5, 12.6.6 and 12.6.7 converges for every real number x.arrow_forward
- use Corollary 12.6.2 and 12.6.3 to derive 12.6.4,12.6.5, 12.6.6 and 12.6.7arrow_forwardExplain the focus and reasons for establishment of 12.5.1(lim(n->infinite) and sigma of k=0 to n)arrow_forwardExplain the focus and reasons for establishment of 12.5.3 about alternating series. and explain the reason why (sigma k=1 to infinite)(-1)k+1/k = 1/1 - 1/2 + 1/3 - 1/4 + .... converges.arrow_forward
- Explain the key points and reasons for the establishment of 12.3.2(integral Test)arrow_forwardUse identity (1+x+x2+...+xn)*(1-x)=1-xn+1 to derive the result of 12.2.2. Please notice that identity doesn't work when x=1.arrow_forwardExplain the key points and reasons for the establishment of 11.3.2(integral Test)arrow_forward
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