Question

In Exercises 33-40, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function Point 8 33. $f(x) = \frac{8}{x^2}$ (2, 2) 3 34. $f(t) = 3 - \frac{3}{5t}$ $(\frac{3}{5}, 2)$ 35. $f(x) = -\frac{1}{2} + \frac{7}{5}x^3$ $(0, -\frac{1}{2})$ 36. $f(x) = 3(5 - x)^2$ (5, 0) 37. $f(\theta) = 4 \sin \theta - \theta$ (0, 0) 38. $g(t) = -2 \cos t + 5$ $(\pi, 7)$ 39. $f(t) = \frac{1}{4}e^t$ $(0, \frac{1}{4})$ 40. $g(x) = -4e^x$ $(1, -4e)$

          In Exercises 33-40, find the slope of the graph of the function at
the given point. Use the derivative feature of a graphing utility
to confirm your results.
Function
Point
8
33. $f(x) = \frac{8}{x^2}$
(2, 2)
3
34. $f(t) = 3 - \frac{3}{5t}$
$(\frac{3}{5}, 2)$
35. $f(x) = -\frac{1}{2} + \frac{7}{5}x^3$
$(0, -\frac{1}{2})$
36. $f(x) = 3(5 - x)^2$
(5, 0)
37. $f(\theta) = 4 \sin \theta - \theta$
(0, 0)
38. $g(t) = -2 \cos t + 5$
$(\pi, 7)$
39. $f(t) = \frac{1}{4}e^t$
$(0, \frac{1}{4})$
40. $g(x) = -4e^x$
$(1, -4e)$

In Exercises 33-40, find the slope of the graph of the function at
the given point. Use the derivative feature of a graphing utility
to confirm your results.
Function
Point
8
33. f(x) = (8)/(x^2)
(2, 2)
3
34. f(t) = 3 - (3)/(5t)
((3)/(5), 2)
35. f(x) = -(1)/(2) + (7)/(5)x^3
(0, -(1)/(2))
36. f(x) = 3(5 - x)^2
(5, 0)
37. f(θ) = 4 sinθ - θ
(0, 0)
38. g(t) = -2 cos t + 5
(π, 7)
39. f(t) = (1)/(4)e^t
(0, (1)/(4))
40. g(x) = -4e^x
(1, -4e)

Added by Eric R.

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