AP CALCULUS AB Derivatives of Inverses 1. Given that f and g are inverses, then f[g(x)]...

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AP CALCULUS AB Derivatives of Inverses 1. Given that f and g are inverses, then f[g(x)] = x Find the derivative of that composition: Solve for g'(x) 2. Given f(x) = 3x-2 for x0 find (f(x)) '(2) 3. Given f(x) = x+3x+1, find (f(x)) '(5). Name Date 4. Given g(x) is a monotonically increasing function, find (g)(-4) based on the table below. Show how you arrived at your answer. 8 X2600 g(x) g'(x) -4 3 2 5 6 7 5. Given y-4=-(x-1) is the equation of a tangent line to f(x), the inverse of function f(x), write 3 the equation of the tangent line to function f(x) at x = 4. f(x) 5 6 f(x) = x+2 is graphed above containing the points (1, 3) and (2,6). 1. Find f'(x) = x = 1: , f'(1)= Write the equation of the tangent line to f(x) at Graph the line on the above grid. Find f(x) = Graph f(x) on the grid above. The point (1, 3) is on f(x) and the point (3, 1) is on the inverse, f(x). Find (f)'(x) = -, (f)'(3)=- Write the equation of the line tangent to the inverse at x = 3: . Graph the line. 2. Find f'(2)=_ Write the equation of the tangent line to f(x) at x = 2 : Graph the line on the above grid. The point (2, 6) is on f(x) and the point (6, 2) is on the inverse, f(x). Find (f) '(6) = Write the equation of the line tangent to the inverse at x = 6: 3. Given g(3) = 4 is on the curve and (4, 3) is on the inverse. If g'(3) = 6, find (g)'(4) = AP CALCULUS AB Derivatives of Inverses 1. Given that f and g are inverses, then f[g(x)] = x Find the derivative of that composition: Solve for g'(x) 2. Given f(x) = 3x-2 for x0 find (f(x)) '(2) 3. Given f(x) = x+3x+1, find (f(x)) '(5). Name Date 4. Given g(x) is a monotonically increasing function, find (g)(-4) based on the table below. Show how you arrived at your answer. 8 X2600 g(x) g'(x) -4 3 2 5 6 7 5. Given y-4=-(x-1) is the equation of a tangent line to f(x), the inverse of function f(x), write 3 the equation of the tangent line to function f(x) at x = 4. f(x) 5 6 f(x) = x+2 is graphed above containing the points (1, 3) and (2,6). 1. Find f'(x) = x = 1: , f'(1)= Write the equation of the tangent line to f(x) at Graph the line on the above grid. Find f(x) = Graph f(x) on the grid above. The point (1, 3) is on f(x) and the point (3, 1) is on the inverse, f(x). Find (f)'(x) = -, (f)'(3)=- Write the equation of the line tangent to the inverse at x = 3: . Graph the line. 2. Find f'(2)=_ Write the equation of the tangent line to f(x) at x = 2 : Graph the line on the above grid. The point (2, 6) is on f(x) and the point (6, 2) is on the inverse, f(x). Find (f) '(6) = Write the equation of the line tangent to the inverse at x = 6: 3. Given g(3) = 4 is on the curve and (4, 3) is on the inverse. If g'(3) = 6, find (g)'(4) =