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Questions 2 and 3 refer to the table below. \begin{tabular}{|c|c|c|c|c|c|c|} \hline $x$ & $-2$ & $-1$ & $0$ & $1$ & $2$ & $3$ \\ \hline $f(x)$ & $2$ & $1$ & $0$ & $-2$ & $3$ & $-1$ \\ \hline $f'(x)$ & $-2$ & $3$ & $1$ & $0$ & $-1$ & $2$ \\ \hline $g(x)$ & $0$ & $-2$ & $2$ & $-1$ & $3$ & $1$ \\ \hline $g'(x)$ & $-1$ & $0$ & $3$ & $1$ & $-2$ & $2$ \\ \hline \end{tabular} 2. (2 marks) Calculate $(fg)'(1)$. A $-2$ \quad B $-1$ \quad C $0$ \quad D $1$ \quad E $2$ \quad F None of these 3. (2 marks) Calculate $\left(\frac{f}{g}\right)'(-1)$. A $\frac{3}{4}$ \quad B $0$ \quad C $-\frac{2}{3}$ \quad D $-\frac{3}{2}$ \quad E DNE \quad F None of these

          Questions 2 and 3 refer to the table below.
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$x$ & $-2$ & $-1$ & $0$ & $1$ & $2$ & $3$ \\
\hline
$f(x)$ & $2$ & $1$ & $0$ & $-2$ & $3$ & $-1$ \\
\hline
$f'(x)$ & $-2$ & $3$ & $1$ & $0$ & $-1$ & $2$ \\
\hline
$g(x)$ & $0$ & $-2$ & $2$ & $-1$ & $3$ & $1$ \\
\hline
$g'(x)$ & $-1$ & $0$ & $3$ & $1$ & $-2$ & $2$ \\
\hline
\end{tabular}
2. (2 marks) Calculate $(fg)'(1)$.
A $-2$ \quad B $-1$ \quad C $0$ \quad D $1$ \quad E $2$ \quad F None of these
3. (2 marks) Calculate $\left(\frac{f}{g}\right)'(-1)$.
A $\frac{3}{4}$ \quad B $0$ \quad C $-\frac{2}{3}$ \quad D $-\frac{3}{2}$ \quad E DNE \quad F None of these

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Questions 2 and 3 refer to the table below.

x -2 -1 0 1 2 3

f(x) 2 1 0 -2 3 -1

f'(x) -2 3 1 0 -1 2

g(x) 0 -2 2 -1 3 1

g'(x) -1 0 3 1 -2 2

2. (2 marks) Calculate (fg)'(1).
A -2 B -1 C 0 D 1 E 2 F None of these
3. (2 marks) Calculate ((f)/(g))'(-1).
A (3)/(4) B 0 C -(2)/(3) D -(3)/(2) E DNE F None of these

Added by Ian G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Kumareshwaran Rathinasabapathy

01/09/2022

Step 1

From the table, we have: f(1) = 1 g(1) = 2 Now, we can use the product rule for differentiation: (fg)'(x) = f'(x)g(x) + f(x)g'(x) So, (fg)'(1) = f'(1)g(1) + f(1)g'(1) We need to find f'(1) and g'(1) from the table: f'(1) = 2 g'(1) = 3 Now we can Show more…

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Questions 2 and 3 refer to the table below. (2 marks) Calculate (fg)^(')(1). (A) -2 (B) -1 (C) 0 (D) 1 (E) 2 (F) None of these (2 marks) Calculate ((f)/(g))^(')(-1) (A) (3)/(4) (B) 0 (C) -(2)/(3) (D) -(3)/(2) (E) DNE (F) None of these Questions 2 and 3 refer to the table below T 2 1 0 1 2 3 f(x) f(x) g(x) g(x) 2 1 0 2 3 1 2 3 1 0 1 2 0 2 2 1 3 1 -1 0 3 1 2 2 . (2 marks) Calculate (fg)'(1) E 2 F None of these . (2 marks) Calculate 3 A I4 2 3 3 2 0 D E DNE F None of these

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00:01 Let's evaluate the expressions using the table values.

00:05 So we do part a.

00:06 In part a we have f -o -g of 1.

00:10 So this equals, according to the composition of function, this is written as f -of -g -of -g -of -1.

00:18 So first we have to find a g -of -1 from the table.

00:22 So we look into the g -of -x row and x equal to one column.

00:27 So that is, g of 1 is 0.

00:29 So therefore this becomes f of 0 which means we have to find the value of the function f of x at x equal to 0 that is equal to 4 so we say that f o g of 1 equals 4 let's do part b in part b we have f o g of 2 so first we write down this as f of g of 2 which means we have to first to find g of 2 from the table so we look into the row for g of x and x equal to 2, which means negative 3.

01:10 So it is f of negative 3.

01:13 So we find f of x and x equal to negative 3.

01:18 So it is 10.

01:19 So f of negative 3 equals 10.

01:22 So therefore this value, f of f, f, g 2 is less to part c.

01:31 So in part c we have gof of 2.

01:38 So first we write down this as g of f of 2.

01:46 So first we have to find f of 2 using the table.

01:50 So we look into the row for f of x at x equal to 2 and this equals 0.

01:56 So therefore this becomes g of 0.

01:59 So we look into the row of g of x at x equal to 0 and this equals 3.

02:06 So therefore g .o .f of 2 is 3.

02:10 We now do part d.

02:14 In part d we have g o f of 3...

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