Chapter 2: Q.27 (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:
$i f f (x) = \frac{3 h (x)}{g (x) + j (x)}, f i n d f' (0) .$

Short Answer

Expert verified

The value of $f' (0)$ is 162

Step by step solution

Step1. Given information

Values of the function and its derivative given.

We have to find out the values of $f' (0)$

Step 2. Differentiate using the quotient rule

$The quotient rule : If f and g are functions and both f and g are differentiable, then quotient rule {(\frac{f}{g})}^{'} (x) = \frac{f (x)' g (x) - f (x) g (x)'}{(g {(x))}^{2}} Let f (x) = 3 h (x) g (x) = g (x) + j (x) when we apply quotient rule then fiven function f' (x) = \frac{3 h' (x) (g (x) + j (x)) - 3 h (x) (g' (x) + j' (x))}{{(g (x) + j (x))}^{2}} then, f' (0) = \frac{3 h' (0) (g (0) + j (0)) - 3 h (0) (g' (0) + j' (0))}{{(g (0) + j (0))}^{2}} from the given table we get values of h' (0) = 3, g (0) = 2, j (0) = 0, g' (0) = - 2 . j' (0) = - 2 and h (0) = 3 Substitute these values in f' (0), then we get f' (0) = \frac{3 \times 3 (2 + 0) - 3 \times 3 (- 2 - 2)}{{(2 + 0)}^{2}} = \frac{18 + 36}{4} = 162$

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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:
$i f f (x) = \frac{3 h (x)}{g (x) + j (x)}, f i n d f' (0) .$

Short Answer

Step by step solution

Step1. Given information

Step 2. Differentiate using the quotient rule

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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)=3h(x)g(x)+j(x),findf'(0).

Short Answer

Step by step solution

Step1. Given information

Step 2. Differentiate using the quotient rule

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Probability and Statistics

Discrete Mathematics

Geometry

Statistics

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:
$i f f (x) = \frac{3 h (x)}{g (x) + j (x)}, f i n d f' (0) .$