Question

Can someone please help me with this

Answer 1

21.
`f'''(x) =-(-2)x^(-3) +2 =2x^(-3) +2`

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.

Explanation:

21. It is given that,
`f'(x) =x^(-1)+x^(2)`

⇒
`f''(x) = -x^(-2) +2x` {Differentiating with respect to x}

⇒
`f'''(x) =-(-2)x^(-3) +2 =2x^(-3) +2` {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)