Math Help - Urgent!! 2 Multiple choice, Tangents

1. Urgent!! 2 Multiple choice, Tangents

The equation of the tangent to the curve y= xsinx at the point (π/2, π/2) is

a) y= x- π
b) y= .5
c) y= π- x
d) y=x+ .5
e) y= x

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If m1 is the slope of the curve xy=2 and m2 is the slope of the curve x^2+y^2=3, then the point of intersection of the two curves is:

a) m1= - m2
b) m1*m2= -1
c) m1= m2
d) m1*m2 = 1
e) m1*m2 = -2

2. Hello,

The equation of a tangent to a function in a point is :

$y=f'(a)(x-a)+f(a)$

$f(\pi/2)=\pi/2$
As $f(x)=xsin(x)$, $f'(x)=sin(x)+xcos(x)$

Hence $f'(\pi/2)=1$