Answer:
21. [tex]f'''(x) =-(-2)x^{-3} +2 =2x^{-3} +2[/tex]
22. y² = 4a ( x + 2 ) is f' and the other one is f
23. a. At x = -1
23. b. At x = -3, -1, and 2.
Step-by-step explanation:
21. It is given that, [tex]f'(x) =x^{-1}+x^{2}[/tex]
⇒ [tex]f''(x) = -x^{-2} +2x[/tex] {Differentiating with respect to x}
⇒ [tex]f'''(x) =-(-2)x^{-3} +2 =2x^{-3} +2[/tex] {Again differentiating with respect to x} (Answer}
22. One of the graph is a parabola having equation y² = 4a ( x + 2 ) .......... (1) , where a is a constant.
If this is f then f' will be a linear equation i.e. a straight line but the other graph is not linear.
Therefore, equation (1) is f' and the other one is f. (Answer)
23. a. h(x) is not continuous at x = -1
23. b. h(x) is not differentiable at x = -3, -1 and 2 (Answer)
