Find two explicit functions by solving the equation for y in terms of x,

Question

(a) Find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx and show that the result is equivalent to that of part (c).

16x2 + 25y2 = 400

Answer 1

Step 1 :

(a)

The function is .

Solve for y in terms of  x.

Divide each side by 25 .

So it has two explicit functions.

and .

Answer 2

Step 2 :

(b)

Now sketch the graph of above two explicit equations .

Step 3 :

(c)

Now find derivative of explicit function .

Similarly .

Hence .

Answer 3

Step 4 :

(d)

Now differentiate the function .

Apply derivative with respect to x.

Derivative of function is  .

Answer 4

Solutions :

(a) Two explicit functions are  and .

(b) Graph of two explicit equations is

(c) Derivative of explicit functions are and .

(d) Derivative of function is  .