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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

Produce graphs of f that reveal all the important aspects of the curve. Use graphs of f′ and f″ to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and inflection points. In Exercise 35 use calculus to find these quantities exactly.

f(x) = x2 + 6.5 sin x, −5 ≤ x ≤ 5

To determine

To sketch: The graph of the given function f(x)=x2+605sinx on the interval [5,5] so that all the important aspects of the graphs are visible.

Explanation

Use online graphing calculator to plot the graph of the function f(x)=x2+605sinx as shown in below Figure 1.

In the above Figure 1 the point (2.4,10.15) is a point of local maxima and (1.2,4.62) and (3.24,9.86) are points of local minima.

Also graph shows that there is no asymptote to the graph.

Differentiate the given function with respect to x.

f(x)=x2+6.5sinxf(x)=2x+6.5cosx

Therefore, f(x)=2x+6.5cosx .

Plot the graph for f(x) with the help of online graphing calculator as shown in below Figure 2.

From the graph observe that function is increasing on the interval (1

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