Please help with the following questions if you can, thank you!

1. Forthe function ffx) = x4 determine an approximation for the slope of the tangent to the curve at the point where a= 0.5. Use w, and h = 0.1. Show all your steps. 2. a) For the function my find an expression for the slope of a tangent at any using W- Simplify the expression. This is a function for slope of the function. Then evaluate this expression by substituting a = 1. Note : What you are doing here is nding the value of the slope ofthe tangent of f(x)= 1h?2 at the point x = 1. b) Determine the equation of this tangent line (in the form y = mx + b) using the slope of the tangent line of f(x) = 1ix2 at the point x = 1 or (1,1) 3. Ascience protect studying catapults sent a proectile into the air with an initial velocity of 30 m/s. The formula for distance (3) in meters with respect to time in seconds is s(t) = -4.9t2 + 301'. Find the instantaneous rate of change (the velocity function) at any time using . [huh-u) igljP: - Determine the instantaneous rate of change (ie. the velocity} at: a) t = 2 b) t = 5 Video Lesson/YouTube support: Students may want to watch the instructor's You Tube video on E vaiuating Limits of Function before attempting this next question. This video can be here. 4. Evaluate the following limits {3-}; it a\" h. a) lirn h> . :1:2 TI 12 b) 111ml; 1316 . :3 5 c) 1.11.11;z IL; I:: d lim 3'1 ) :z>1 121 e) lim J#"":_ E Iii' 1- a. Find the slope of the tangent to the curve y = x4 - 5x2 + 3 to complete the [-3 following table. . i d. D W? b. Sketch a graph of the derivative and find the equation for that function- Please make sure that you show your work when finding the equation of this derivative function {linear regression using Excel, Desmos or another online tool ; or by solving a system of equations using the General Equation and the points from the table of values (above)). E2. Create an equation of the form y = ax3 + bx2 + or +d where a, b, c, and d are not ' zero. Graph this equation and nd the slope of the tangent to this curve to complete the following table. a. Use appropriate values for x. % W? ll ll | l | l b. Sketch a graph of the derivative and find the equation for that function. Please make sure that you show your work when nding the equation of this derivative function (linear regression using Excel, Desmos or another online tool ; or by solving a system of equations using the General Equation and the points from the table of values (above))