Consider the function f(x)=-x^4+ax^2+5 where a is a constant. Part of the graph of y=f(x) is shown below. There are two other points on the graph of y=f(x) at which the tangent is horizontal D) I. Write down the x-coordinates of these two pointsII. Write down the intervals where the gradient of the graph y=f(x) is positive E) Write down the range of f(x) F) Write down the number of solutions to the equation f(x)=5

Ch 13: Properties of Curves Name: are Hoffman ASSESSMENT 1 ) Consider the function f(x) =- x + ax + 5, where a is a constant. Part of the graph of y = f(x) is shown below. a) Write down the y-intercept of the graph. [1] b) Find f' (x). [2] It is known that at the point where x = 2 the tangent to the graph of y = [(x) is horizontal. c) i) Show that a = 8. [2] ii) Find f (2) [2] There are two other points on the graph of y = f(x) at which the tangent is horizontal. d) i) Write down the x-coordinates of these two points [2] ii) Write down the intervals where the gradient of the ph ofy = f(x) [2] is positive. e) Write down the range of f (x) [2] f) Write down the number of solutions to the equation f (x) = 5 [1]