YU The Number of Possible Solutions to The Equation Question

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12g. [2 marks]
Write down the range of f(x).
12h. [1 mark]
Write down the number of possible solutions to the equation f(x) = 5.
12i. [2 marks]
The equation f(x) = m, where me R, has four solutions. Find the possible values of m.
12d. [2 marks]
Find f(2).
12e. [2 marks]
There are two other points on the graph of y = f(x) at which the tangent is horizontal.
Write down the x-coordinates of these two points;
12f. [2 marks]
Write down the intervals where the gradient of the graph of y = f(x) is positive.
nolia bin icon
1d. [1 mark]
Hence explain why the graph off has a local maximum point at x = a.
A functia f has a local marmun at a
point xta if the values flot of f for X near
xiza ove all less than f (80) Thus
, the graph
of near xa has a peak at at x = a’
1e. [3 marks]
Find f”(b).
f'(x) = 2xth
f” (3)= 2X34758
1f. [1 mark]
Hence, use your answer to part (e) to show that the graph off has a local minimum point at
x= b.
f )
+13= 1 / 3 x 3 ² + 3 ² -45 H7
=979-46417
🙂
local min; ( 3,/0)
1g. (5 marks]
The normal to the graph of f at x = a and the tangent to the graph off at x = b intersect at
the point (p. 9).
Find the value of p and the value of q.
X=a= -3
i p=-5 , q=10
12. NO CALCULATOR
12a. [1 mark]
Consider the function f(x) = -x4 + ax2 + 5, where a is a constant. Part of the graph of y =
f(x) is shown below.
Write down the y-intercept of the graph.
M
12b. [2 marks]
Find f'(x).
12c. [2 marks]
It is known that at the point where x = 2 the tangent to the graph of y = f(x) is horizontal.
=
Show that a = 8.
2
3c. [2 marks]
Find the equation of the tangent to the graph off at A.
3d. [5 marks]
Find the coordinates of B.
3e. [2 marks]
Find the rate of change of f at B.
4. We will do this one later with optimization