Assignment:
Q1. Find dy/dx
5x 4/5 + 10y 6/5 = 15
Q2. a. By differentiating x 2 - y2 =1 implicitly, show that dy/dx = x/y
b. Then show that d2y/dx2 = - 1/y3.
Numerical Values of Derivatives
Q3. Suppose that the function f(x) and its first derivative have the following values at
x = 0 and x = 1
|
x
|
f(x)
|
f'(x)
|
|
0
|
9
|
-2
|
|
1
|
-3
|
1/5
|
Find the first derivatives of the following combinations at the given value of x
a. √x f(x), x = 1
b. √f(x) , x = 0
c. f(√x) , x =1
d. f(1 - 5 tan x), x = 0
e. f(x) / 2+cosx , x = 0
f. 10sin (πx/2)f2(x), x = 1
Q4. If x1/3 + y1/3 = 4, find d2y/dx2 at the point (8,8)
Q5. For what value or values of the constant m, if any is
f(x) = {sin 2x , x≤0
{mx , x>0
a. continuous at x = 0?
b. differentiable at x = 0?
Give reasons for your answers.
Provide complete and step by step solution for the question and show calculations and use formulas.