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We are supposed to explain why the given function can be expressed in form , when
.
Since the given function is an exponential function we can express it as .
Now let us substitute x=0 in the given function,
Let us substitute x=0 in our function.
Upon substituting a=1 in our function we will get,
Therefore, our function f can be represented by the formula of the form .
The table is attached in the figure.
g(x) = f(4x) ⇒⇒⇒ differentiating both sides with respect to x
∴ g'(x) = ⇒⇒⇒⇒⇒⇒ chain role
To find g '(0.1)
Substitute with x = 0.1
from table:
f'(0.1) = 1 ⇒ from the table
∴ g'(0.1) = 4 * [ f'(0.1) ] = 4 * 1 = 4
