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Lesechka [4]
3 years ago
6

6. Let f and g be differentiable functions

Mathematics
1 answer:
Julli [10]3 years ago
5 0

Answer:

(b) 1

Step-by-step explanation:

To differentiate h(x)=f(x)g(x) we will need the product rule:

h'(x)=f'(x)g(x)+f(x)g'(x).

We have h'(x)=f(x)g'(x), so the following equation is true by the transitive property:

f'(x)g(x)+f(x)g'(x)=f(x)g'(x)

By subtraction property we have:

f'(x)g(x)=0

Since g(x) \neq 0, then we can divide both sides by g(x):

f'(x)=\frac{0}{g(x)}

f'(x)=0

This implies f(x) is constant.

So we have that f(x)=c where c is a real number.

Since f(0)=1 and f(0)=c, then by transitive property 1=c.

So f(x)=1.

Checking:

h(x)=1 \cdot g(x)

h'(x)=g'(x)=1 \cdot g'(x)

So the following conditions were met.

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