Does the rule y=6x^7 represent an exponential function
2 answers:
An exponential function is a function in which the variable is in the exponent.
Functions of the type :
Here the exponent is an integer.
Such functions are called Arithmetic functions.
Functions of the type
y = 2 ^x
Here the exponent of 2 is a variable.
Such functions are called exponential functions
We are given y =6 x^7.
Here the variable is base & the exponent is an integer.
So does not represent an exponential function.
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Answer:
The minimum surface area of the container is 276.791 square units.
Step-by-step explanation:
Let be ,
,
. The first and second derivatives of such function are, respectively:
First derivative
Second derivative
The critical values of are determined by equalizing first derivative to zero and solving it: (First Derivative Test)
(since radius is a positive variable)
To determine if critical value leads to an absolute minimum, this input must be checked in the second derivative expression: ()
The critical value leads to an absolute minimum, since value of the second derivative is positive.
Finally, the minimum surface area of the container is:
The minimum surface area of the container is 276.791 square units.