Find the points of inflection of the graph of the function. f(x) = 7 sin x + sin 2x, [0, 2\pi]...

Question:

Find the points of inflection of the graph of the function.

f(x) = 7 sin x + sin 2x, {eq}[0, 2\pi] {/eq}

(x, y)= ( ) (smallest x-value)

(x, y)= ( ) (largest x-value)

Inflection point

A function with one independent variable has an inflection point where its second derivative is zero, therefore an inflection point is found solving the second derivative expression, or with the second derivative graph, identifying the x-axis interceptions.

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The function is:

{eq}\displaystyle \ f(x) = 7 sin x + sin 2x \\ {/eq}

The first derivative is:

{eq}\displaystyle \ f'(x)= 7\,\cos \left(...