Given-f-x-1-3-x-2x-Ax-4-x-2-if-f-1-5-then-A-floor-function-

Question Number 183158 by cortano1 last updated on 21/Dec/22

G i v e n f (x) = \frac{[\frac{1}{3} x] ∣ 2 x ∣ + A x}{∣ 4 - x^{2} ∣}

i f f^{'} (- 1) = 5 t h e n A = ?

[] = f l o o r f u n c t i o n

Answered by TheSupreme last updated on 21/Dec/22

f (x) = \frac{g (x) h (x)}{u (x)} + \frac{A x}{4 - x^{2}}

f^{'} (- 1) = \frac{(g^{'} (x) h (x) + g (x) h^{'} (x)) u (x) - g (x) h (x) u^{'} (x)}{u^{2} (x)} + A \frac{4 - x^{2} - 2 x^{2}}{{(4 - x^{2})}^{2}} =

g^{'} (- 1) = 0

g (- 1) = - 1

h^{'} (- 1) = 2

h (- 1) = 2

u^{'} (- 1) = 6

u (- 1) = 3

f^{'} (x) = \frac{(- 2 + 2) 3 + 2 * 6}{3^{2}} + A \frac{1}{9} = 5

12 + A = 45 \to A = 32

Commented by greougoury555 last updated on 22/Dec/22

w h a t t h e f o r m u l a \frac{d [\frac{1}{3} x]}{d x} = ?