Chapter 2: Q.28 (page 198)

Suppose g(x), h(x), and j(x) are differentiable functions with
values of the function and its derivative given in the following table:
$i f f (x) = \frac{g (x) h (x) + j (x)}{h (x)} f i n d f' (- 1)$

Short Answer

Expert verified

The value of $f' (- 1)$ is $- 1 + \frac{2}{0}, here \frac{2}{0} is not defined$

Step by step solution

Step1. Given information

Values of the function and its derivative given.

We have to find out the values of $f' (- 1)$

Step 2. Finding the derivatives of the given function

Here $f (x) = \frac{g (x) h (x) + j (x)}{h (x)}, = g (x) + \frac{j (x)}{h (x)} When we do differentiation, we get f' (x) = g' (x) + {(\frac{j (x)}{h (x)})}^{'} By applying the quotient rule, we get {(\frac{j (x)}{h (x)})}^{'} = \frac{j' (x) h (x) - j (x) h' (x)}{(h {(x))}^{2}} since the quotient rule : {(\frac{f}{g})}^{'} (x) = \frac{f (x)' g (x) - f (x) g (x)'}{(g {(x))}^{2}} then f' (x) = g' (x) + \frac{j' (x) h (x) - j (x) h' (x)}{(h {(x))}^{2}}$

Step 3. Finding the value of f'(-1)

$Since f' (x) = g' (x) + \frac{j' (x) h (x) - j (x) h' (x)}{(h {(x))}^{2}} then f' (- 1) = g' (- 1) + \frac{j' (- 1) h (- 1) - j (- 1) h' (- 1)}{(h {(- 1))}^{2}} From the table we get values, g' (- 1) = - 1, j' (- 1) = - 2, h' (- 1) = - 2, j (- 1) = 1, h (- 1) = 0 substitute these values on f' (- 1) . then we get f' (- 1) = g' (- 1) + \frac{j' (- 1) h (- 1) - j (- 1) h' (- 1)}{(h {(- 1))}^{2}} = - 1 + \frac{- 2 \times 0 - 1 \times - 2}{0^{2}} = - 1 + \frac{2}{0}, here \frac{2}{0} is not defined$

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Suppose g(x), h(x), and j(x) are differentiable functions with
values of the function and its derivative given in the following table:
$i f f (x) = \frac{g (x) h (x) + j (x)}{h (x)} f i n d f' (- 1)$

Short Answer

Step by step solution

Step1. Given information

Step 2. Finding the derivatives of the given function

Step 3. Finding the value of f'(-1)

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Suppose g(x), h(x), and j(x) are differentiable functions withvalues of the function and its derivative given in the following table:iff(x)=g(x)h(x)+j(x)h(x)findf'(-1)

Short Answer

Step by step solution

Step1. Given information

Step 2. Finding the derivatives of the given function

Step 3. Finding the value of f'(-1)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Suppose g(x), h(x), and j(x) are differentiable functions with
values of the function and its derivative given in the following table:
$i f f (x) = \frac{g (x) h (x) + j (x)}{h (x)} f i n d f' (- 1)$