a. Find the derivative function f' for the functionf. b. Find an equation of the line tangent to the graph of f at (a, f(a)) for the given value of a. 1 ; a =-1 X + 3 5) f(x) = A) a. f'(x) = (x + 3)2 3 b. tangent line is y =x+ 4 4 %3D B) a. f'(x) = ; b. tangent line is y X + 4 (x + 3)2 1 1 3 C) a. f'(x) = -- (x + 3)2 b. tangent line is y = -7** 7 D) a. f (x) b. tangent line is y = - x- 2 1/4

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A: Thanks for your patience!Kindly comment if you need any clarifications.

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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: