Thread: Help me with these differentiation problems please!

a) If e^2-e^x
Find any stationary points on the curve. (Also how would I go about drawing this curve?)

b) The curve y=ln(x^2-3) crosses x axis at (2,0) and (-2,0). The normals at A and B meet at P. Find the coordinates of P.

c) If y=asinnx +bcosnx show that d^2y/dx^2+n^2y=0

thanks in advance

Originally Posted by Confuzzled?

a) If e^2-e^x
Find any stationary points on the curve. (Also how would I go about drawing this curve?)

thanks in advance

differentiating the function with respect to x we get
-e^x
for stationary point it has to be zero
which is possible only if x is a very large negative number

graph of the function
Are you familiar with the transformation of graph?
If yes, here is how to graph your function

graph e^x
transform to -e^x
tranform to -e^x + e^2

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Malay

Originally Posted by Confuzzled?

a
b) The curve y=ln(x^2-3) crosses x axis at (2,0) and (-2,0). The normals at A and B meet at P. Find the coordinates of P.


thanks in advance

i hope A is (2,0) and B is (-2,0)

for P, we have to find the equations of the normals at A and B
Normal passing through A
Slope of tangent at A=2x/(x^2-3) where x=2 comes out to be 4
slope of normal will be -1/4
hence equation is (y-0)/(x-2) = -1/4
4y=2-x
x+4y=2

Normal passing through B
slope of tangent at B=-4
slope of normal at b=1/4
hence equation is (y-0)/(x+2) = 1/4
4y=x+2
x-4y=-2

the intersection point of the two normals come out to be (0,1/2) which is your P

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Malay