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Note: Proper form is important!!! Show work for marks! 5. The position function of a particle is given by s(t) = t' - 121 + 45t + 3, where time, t, is in seconds, and distance, s, is in metres, and t 2 0. Find the velocity of the particle when the acceleration is zero. 1. Differentiate. DO NOT SIMPLIFY ! ! ! (a) f(x) = 5- 7(x-2)(x-3) (b ) (3 + 4x) 3 (c) f (t ) = 15 - 70 (d) y= +-+ 6. A company sells an average of 50 skateboards per month at a price of $120 each. For each $5 decrease in price, two more skateboards are sold. (a) Determine the price function, pul let u represent the numberit $5 decreases in price. (e ) f( x ) = 3x - 4 (use quotient rule ) (b) Determine the revenue function. (or ) (c) Determine the marginal revenue when 25 skateboards are sold. 2. Determine f"(1) for the function f(x) = (3x2 -5x). (d) At what price will the skateboards sell at when 25 skateboards are sold? A (A) nad x atx = 4ify - Today and u- VI-1. ( use herbrizz notation ) 3. Find the equation of the tangent line to the curve f(x) = x' +2 (x3 +3x-1 at x= 0. w j 8. Given y = 2x3 - 5x, determine the slope of the tangent line(s) at the x- intercepts. 4. The position function of an object thrown on the moon is given by (T) s(t) = 6.5t - 0.831", where time, t, is in seconds and distance, s, is in metres. Find the maximum height of the object.(Use calculus )