Differentiation turning points practice, Exercises of Mathematics

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P2 Text Differentiation – Turning Points

P2 Text Differentiation - Turning Points > Tat) (78) BEE EXECUTIVE FUNCTION Find the least vah f the foll functi in e least value of the following functions: ap For each part of a f(x) =x? - 12x +8 b f(x) =x? -8x-1 questions 1 and 2: © f(x) =5x? + 2x @ Find f’(Q). @ Set f(x) =0 and solve Find the greatest value of the following functions: to find the value of x a f(x) =10-5x2 b f(x) =34+2x-2 at the stationary point. @ Find the corresponding eK) = 6421-9) value of f(x). 3 Find the coordinates of the points where the gradient is zero on the curves with the given equations. Establish whether these points are local maximum points, local minimum points or points of inflection in each case. a p=4x°+ 6x b yp=94xN-X* ¢ pax -x4+1 d y=x(x? - 4x -3) eyaxtt f yore g y=x-3Vx h y=x7(x-6) i p=xt- 122 4 Sketch the curves with equations given in question 3 parts a, b, ¢ and d, labelling any stationary points with their coordinates. ® 5 By considering the gradient on either side of the stationary point on the curve y= x5 - 3x? + 3.x, show that this point is a point of inflection. Sketch the curve y = x? — 3x? + 3x. ® 6 Find the maximum value and hence the range of values for the function f(x) = 27 - 2x4. © 7 fx) ext430-5x°- 3x41 cp Use the factor theorem a Find the coordinates of the stationary points of f(x), with small positive integer and determine the nature of each. values of x to find one factor b Sketch the graph of y = f(x). off). © Pure 2 Section 7.2