Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function f(x) = 2(x − 4)2 Point (2, 8)
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function f(x) = 2(x − 4)2 Point (2, 8)
Given:
The function,
f(x) = 2(x − 4)2
The point (2, 8)
Slope of function f(x) at point (a, b) is
= f'(a, b)
f(x) = 2(x − 4)2
f'(x) =4(x - 4)
f'(2, 8) = 4 ( 2 - 4)
f'(2, 8) = - 8
Therefore slope of function f(x) = 2(x − 4)2 at point (2, 8) is -8
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