Find fx using the definition of the derivative and find fx

Question

1. Use the graph of f(x) below to find the following:

(a) lim_x→0' f (x)
(b) lim_x→4⁺ f (x)
(c) lim_x→2 f(x)
(d) lim_x→3 f(x)
(e) lim_x→∞ f(x)
(f) lim_x→-∞ f(x)

(g) points where f is not continuous

(h) points where f is not differentiable

(i) intervals where f'> 0

(j) intervals where f' < 0

(k) intervals where f"> 0

(l) intervals where f" < 0

2. Find the following limits:

(a) lim_x→-1 x² + x/x² - x - 2

(b) lim_x→2 x² + x/ x² -x-2

(c) lim_x→∞ x² + x/ x² -x-2

3. Find f' (x) using the definition of the derivative if f (x) = 3x² -1.

4. Find f'(x) using the rules of derivatives:

(a) f (x) = (x + 2)³(x-3)⁵

(b) f (x)= √(3x² +1)

(c) f (x) = e^2x/6x

(d) f (x) = 3^x -x^1/3

(e) f (x) = ln(√x + 1)

(f) f (x) = 51n(x² - x +3)

(g) f (x) = 3log₂(x)-1

Answer 1

As the following assignment that will describe you about to use of graph 1. Use the graph of f(x) below to find the following: (a) limx?0' f (x) (b) limx?4+ f (x) (c) limx?2 f(x) (d) limx?3 f(x) (e) limx?8 f(x) (f) limx?-8 f(x) (g) Points where f isn’t continuous (h) Points where f isn’t differentiable (i) Intervals where f'> 0 (j) Intervals where f' < 0 (k) intervals where f"> 0 (l) Intervals where f" < 0 2. Discover the subsequent limits: (a) limx?-1 x2 + x/x2 - x - 2 (b) limx?2 x2 + x/ x2 -x-2 (c) limx?8 x2 + x/ x2 -x-2