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Calculus I: Project 3 – Off on a Tangent … Mountain Bike Jumps
1. Design a 4 period sequence of gap jumps as shown
Choose width (W) _______
Choose height (H) _______
Choose period (P) _______
Choose amplitude (A) _______
Choose slope (S) _______
2. Find the equation of a cosine wave to match
the mountain bike trail design
Recall: y = a cos b(x - c) + d:
a = amplitude; b =
; c = horizontal shift; d = vertical shift
3. Find f’(11) and explain its meaning in context in one complete sentence.
4. Find the (x,y) point for the 1st peak & valley after the start, accurate to 3 decimal places.
5. Find the steepest slopes, both positive and negative, accurate to 3 decimal places.
6. Find the parabolic equation modeling the perfect jump (shown in the diagram as a
dashed line) leaving from and returning to, the curve at inflection points. Location
should be clearing the 3rd gap as shown.
7. Graph your functions from (2) and (6) in DESMOS (https://www.desmos.com/calculator)
(Print-screen a picture from Desmos and paste, wrap-text(tight) and crop it in the space
below … with domain restrictions as shown). The trail is green and jump dashed red.
1-page solution for a team of 2 (printed or emailed) due to me by the start of class Wed. 3/18