Express f (x) = |x-5| as a piecewise defined function
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ANSWER
An exponential growth function.
EXPLANATION
The given function is
This function is of the form,
Since k is positive , the function will grow exponentially and fall asymptote to the negative x-axis.
As x-values becomes bigger and bigger positively, the graph grows exponentially.
An exponential growth function.
EXPLANATION
The given function is
This function is of the form,
Since k is positive , the function will grow exponentially and fall asymptote to the negative x-axis.
As x-values becomes bigger and bigger positively, the graph grows exponentially.
a ) The domain:
x^4 - 16 x² ≥ 0
x² ( x² - 16 ) ≥ 0
x² - 16 ≥ 0
x² ≥ 16
x ∈ ( - ∞, - 4 ] ∪ [ 4 , + ∞ )
b ) f ` ( x ) =
= ( 2 x³ - 16 x ) / √(x^4 - 16 x²)
c ) The slope of the tangent line at x = 5:
f ` ( 5 ) = ( 2 * 125 - 16 * 5 ) / √ ( 625 - 400 ) = 170 / 15 = 34 / 3
The slope of the line normal to the graph at x = 5:
m = - 3 / 34