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.

Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

#8.) Determine the slope of the tangent at point (1,4) on the graph of f(x) = (9-x²) ²3/ #10.) a) Determine the values of x where the graph of each function has a horizontal tangent i> y=(x²-435 -ii) y= (x³ -x)² to x + 5y -10 = D. #12.3 A tangent to the parabola y=3x²-7x +5 is perpendicular Determine the equation of the tangent. #13.) The line y = 8x tb tangent to the curve y² 2x². Determine the point of tangency and the value of b #29. Find numbers a, b, and c so that the graph of f(x) = ax² + bx tc has and a tangent with Slope 16 where x = 2 x-intercepts at (0,0) and (8.0)