A maths

bonkysleuth SG

The curve for which dy/dx = x - k/x^2 where k is a constant, is such that the tangent at (3,1) passes through the origin. Find the value of k and the equation of the curve,

Got 24 for value of k. However I do not know how to solve for the equation of curve. Do I use integration? Always have problems solving such questions because I cannot identify whether to use differentiation/integration.. Can someone help? thanks

wee_ws SG

Hi,

Equation of the curve takes the form of y = f(x). Now you are given the expression of dy/dx. Recall that in differentiation we start with y = f(x) and then we proceed to find dy/dx; in integration, we do the reverse.

Thanks!

Cheers,
Wen Shih

wilhelm SG

stupid me.

got rise and run mixed up.

deepak.c SG

dy/dx = x - (24/x^2)

Integrate [x - (24/x^2)] dx = (0.5 x^2) + 24/x + C

Since (3, 1) is a point on the curve,

(0.5*(3)^2) + 24/3 + C = 1

0.5(9) + 24/3 + C = 1

4.5 + 8 + C = 1

C = -11.5

Equation of the curve would be:

y = 0.5x^2 + 24/x -11.5