Question 4, 6,7It’s for my assignment and I need the full work.

Question 4, 6,7It’s for my assignment and I need the full work.


Calculus Assignment
Derivatives!
Work should be your own, although helping each other is encouraged,
each assignment handed in should be unique. If asked, you should be able to
explain or recreate your solution.
1. Find the equation of the normal to y = 8Vx -+1 at the point(s) where x = 16.
4
2. Find the equation(s) of the tangent(s) to 5x – x’y2 = 4y +8 at x = 1
X
4
3
x
+ 2x² +ăbe horizontal?
3. For what value(s) of x will the tangent to y=4
3
4. Local minimax points usually occur when the first derivative is equal to zero.
What are the likely x coordinates of the maximum/minimum points of the function
y = (2 – 5x*)*(3x? -8)?
5. Edna’s swimming pool is being drained (because of an accident) such that the volume
(V) of water (in litres) that remains in the pool after t hours is given by
2
V(t) = 2000 – 20t +=t?.
3
V(10) -V(4)
a) What does the expression
represent? Be precise.
6
V(5+h)-V(5)
b) What does the expression lim
represent? Be precise.
h
c) How much water is in the pool to start?
d) How fast is the water draining after 2 hours?
e) When will the pool stop draining? (When is the drainage rate equal to 0 L/hour ?)
f) When the pool stops draining, is it completely empty? If not, how much water is in
the pool ?
h→0
6. The function y = x4 + 2x” – 27x – 54 intersects the x-axis at 2 points.
Determine the equations of the tangents at these points.
7. The tangent to the function f(x) = 4x² – x+3 at x = 2 hits the function again at one
other point. Determine the slope of the tangent at the other point.
DUE DATE: FRIDAY, MARCH 8th

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