question archive x -3 0 3 4 ¦(x) 5 -1 2 7 ¦’(x) -2 4 0 1 The table above gives values of a twice differentiable function ¦ and its first derivative ¦’ for selected values of x
x -3 0 3 4 ¦(x) 5 -1 2 7 ¦’(x) -2 4 0 1 The table above gives values of a twice differentiable function ¦ and its first derivative ¦’ for selected values of x
Subject:MathPrice: Bought3
|
x |
-3 |
0 |
3 |
4 |
|
¦(x) |
5 |
-1 |
2 |
7 |
|
¦’(x) |
-2 |
4 |
0 |
1 |
The table above gives values of a twice differentiable function ¦ and its first derivative ¦’ for selected values of x. Let g be the function defined by g(x) = ¦(2x – x2).
- What is the value of g’(-1) ?
- It is known that g’’(0) = 0. What is the value of ¦’’(0)?
- Is there a value c, for 0 < c < 3, such that g = 2? Justify your answer.
- Let h be the function with first derivative given by h’ (x) = 4xex. At what value of x in the interval 0 £ x £ 4 does the instantaneous rate of change of h equal the average rate of change of ¦ over the interval 0 £ x £ 4?
