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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Sketch the graph of a function q that is continuous on its domain (–5, 5) and where g(0) = 1, g'(0) = 1, g'(– 2) = 0, lim x 5 + g ( x ) = , a n d lim x 5 g ( x ) = 3.

To determine

To sketch: The graph of a function g.

Explanation

Given:

The function f(x) is continuous on its domain (5,5).

The values. g(0)=1,g(0)=1,g(2)=0,limx5+g(x)=, and limg(x)=3x5.

Calculation:

Here given value g(0)=1,

That is, the point of the graph of the function g(x) is (0,1)

Note that, f(a) means that the slope of the tangent to the function f(x) at the point (a,f(a)).

The given value g(2)=0.

That is, the slopes of tangent to the function g(x) at (2,g(2)) are zero.

Note that, the slope zero at a point means horizontal tangent line at that point.

Thus, the graph of the function g(x) has horizontal tangent at (2,g(2)).

Note that, the value f(a) means that the instantaneous rate of change of y=f(x) at x when x=a

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