Problems 87-94 require the following discussion of a secant line. The slope of the secant line containing the two points ( x , f ( x ) ) and ( x + h , f ( x + h ) ) on the graph of a function y = f ( x ) may be given as In calculus, this expression is called the difference quotient of f (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find m sec for h = 0.5 , 0.1, and 0.01 at x = 1 . What value does m sec approach as h approaches 0? (c) Find an equation for the secant line at x = 1 with h = 0 .01 . (d) Use a graphing utility to graph f and the secant line found in part (c) in the same viewing window. 89. f ( x ) = x 2 + 2 x
Problems 87-94 require the following discussion of a secant line. The slope of the secant line containing the two points ( x , f ( x ) ) and ( x + h , f ( x + h ) ) on the graph of a function y = f ( x ) may be given as In calculus, this expression is called the difference quotient of f (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find m sec for h = 0.5 , 0.1, and 0.01 at x = 1 . What value does m sec approach as h approaches 0? (c) Find an equation for the secant line at x = 1 with h = 0 .01 . (d) Use a graphing utility to graph f and the secant line found in part (c) in the same viewing window. 89. f ( x ) = x 2 + 2 x
Solution Summary: The author explains the function f (x) = x 2 + 2. Calculation requires the discussion of a secant line.
Problems 87-94 require the following discussion of a secant line. The slope of the secant line containing the two points
and
on the graph of a function
may be given as
In calculus, this expression is called thedifference quotient of f
(a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer.
(b) Find msec for
, 0.1, and 0.01 at
. What value does msec approach as h approaches 0?
(c) Find an equation for the secant line at
with
.
(d) Use a graphing utility to graph f and the secant line found in part (c) in the same viewing window.
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rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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