Find the instantaneous rate of change of the function f(x)=3x^2 as x approaches 3.

The instantaneous rate of change as x approaches 3 is 18.

Step-by-step explanation:

From Differential Calculus and Geometry we remember that instantaneous rate of change of the function is represented by a tangent line, whose slope is determined by the first derivative of the curve. Let , the instantaneous rate of change of the function when x approaches 3 is deducted from the definition of derivative:

(1)

(2)

If we know that , then the instantaneous rate of change as x approaches 3 is:

The instantaneous rate of change as x approaches 3 is 18.

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|