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

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(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).

16x+ 25y= 400

asked Jan 22, 2015 in CALCULUS by anonymous

4 Answers

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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 .

answered Jan 22, 2015 by yamin_math Mentor
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Step 2 :

(b)

Now sketch the graph of above two explicit equations .

Step 3 :

(c)

Now find derivative of explicit function .

image

Similarly image.

Hence image.

answered Jan 22, 2015 by yamin_math Mentor
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Step 4 :

(d)

Now differentiate the function .

Apply derivative with respect to x.

image

Derivative of function is  image.

answered Jan 22, 2015 by yamin_math Mentor
edited Jan 22, 2015 by yamin_math
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Solutions :

(a) Two explicit functions are  and .

(b) Graph of two explicit equations is

(c) Derivative of explicit functions are image and image.

(d) Derivative of function is  image.

answered Jan 22, 2015 by yamin_math Mentor

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