Supply what is asked in each item. Show your complete solutions. 1. Given f(x) =x- +4x-5. a) Find the derivative for / (x) using limit definition of the derivative [3 points] b) Find the value of /'(1). [1 point] c) Find the equation of the tangent line to /(x) at the point (1,0) [1 points] 2. Find the derivative of the following functions using the power rule, sum and/or difference rule, and/or the constant rule. a) y= Ax [2 points] b) g(x)_ 3x -6x +2 3. The equation for the height of an object thrown upward with a velocity of 36 m/'s is given by the function h(1)=36 -62. a) Find the equation for the instantaneous velocity of the object. [1 points] b) Find the maximum height reached by the object. [2 points] 4. Given /(x)=x+6x-16 a) Find the derivative of f(x). [1 points] b) Find the equation of the tangent line at (2,0). [2 points] 5. At what points does the curve, y=2x +3x -36x have horizontal tangents? [3 points] 6. Differentiate the following. Simplify your answers (positive exponents or radicals in simplest form). a) y=x(2-x +5x [3 points] b) 1=3 * +4 3x_[ [2 points] c) y=(4x) +5x) [2 points] dx 7. Find " by implicit differentiation. a) 9x3 -16y' =144 [2 points] b) xy =10 [3 points]