Math Is Fun Forum

tonyz1949

Member

Registered: 2007-08-04

Posts: 20

Curves

1. Find the values of a and b such that the function g(x) is continuous everywhere. Justify your answer.

g(x) = 3ax - 2bx² + 1 if x > 2
          2ax - 3            if x = 2
          4ax³ - 5b         if x < 2

2. Consider the curve given by the equation -4y³ + 3xy = -2x -14
   a) Find dy/dx
   b) Write an equation for the line tangent to the curve at the point where y = 1

3. Find dy/dx

a) y = 4(3x+5)cos²x

b) y = (2x+1)^(sinx)

Thanks in advance for helping me

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Curves

1. For g(x) to be continuous everywhere the limit of the function from the left and from the right as x approaches c have to be the same as the function value at c. In this case c being 2. That should help you answer the first question.

2. (a) Use implicit differentiation to find dy/dx

(b) The line tangent to a function is given by y-y1 = m(x - x1), where m is the slope. They tell you the line is tangent at the point y=1 so plug it in and you will get the x value. Now you have you point (x1,y1). In part (a) u had to find dy/dx which is the derivative, plug x1 into dy/dx which will give you the slope.

3. (a) Just use chain rule.

(b) Find the derivative by using the natural log (ln) properties to get rid of the exponential sin(x).