Let f(x) = cos2x - 3sen2x, with 0 ≤ x ≤ π. (a) Find all roots of equation f(x) = 0 (b) (i) Find f '(x)     (ii) From the above, find coordinates of points of graph y = f(x) where f ‘(x) = 0  (c) Draw approximately graph y = f(x), showing CLEARLY coordinates of all points where f ‘(x) = 0 and of all points where graph touches coordinate axes.

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A: Please see the explanation below..

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A: topic - equation of tangent line to curve

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A: Definition used – Extreme values of function – By equating the first derivative to 0, we get…

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A: Given, f'(x) = 4-4x2(x2 +1)2  f''(x) = 8x3 -24x(x2+1)3 (a) If f is concave up then f''(x) >0 So,…

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A: The slope of a line passing through the points  is given by the formulaThe Tangent line to a…

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A: Explanation of the answer is as follows

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A: Solution - Given function - f(x)=x2+36x2 a.)        f'(x)=2x+36-2x-2+1             f'(x)=2x-72x…

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Q: For each function find the indicated expression(Final Form of equation must be simplified

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A: f(x)=(8x-7)(-x+2x2)equation of tangrent line is y=mx+cwhere m is slope of linem=f'(x)

Q: (4) The Temperature T (measured in degrees Fahrenheit) in a growing chamber varies over a 24-hour…

A: Given Tt=68+sinπ12t