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Derivative_Basic_Info_3_pages

# Derivative_Basic_Info_3_pages - I Find the Derivative of a...

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Derivative - Long and short methods 10/12/10 Professor Polenzani I. Find the Derivative of a Function : (The result is a function, not a numerical value – unless the original function is a constant or linear.) A. Short Way – Use the Derivative Rules (Power, Product, Quotient and Chain Rule) Use power rule to find derivative of P (x ) = -x 2 + 12x - 32 P’(x) = -2x + 12 Long way by using the formula: x h x x f h x f h x f + + = ) ( ) ( ) ( 0 ) ( lim II. Find the numerical value of the derivative (slope) at a specific point (x=a value) on the curve. A. Short Way: Use the Derivative Rules (Power, Product, Quotient and Chain Rule) to find the derivative of the function. Then substitute the x=a value into the function to obtain a numerica l value. Part 1 – Method B Use formal definition to find the derivative of this profit function: P(x) = -x 2 + 12x - 32 f(x+h) = -(x+h) 2 +12(x+h)-32 = - x 2 – 2xh – h 2 + 12x + 12h - 32 f(x) = - x 2 + 12x – 32 x h x x f h x f h x f + + = ) ( ) ( ) ( 0 ) ( lim = h 32 + 12x - x + 32 - 12h + 12x + h - 2xh - x - 2 2 2 = 12 2 12 0 2 12 2 ) 12 2 ( 12 2 2 + = + + = + = + = + x x h x h h x

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Derivative_Basic_Info_3_pages - I Find the Derivative of a...

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