MHB Composite Functions and Exponential Growth

ardentmed
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Hey guys,

Few more questions for the problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help.

Question:
08b1167bae0c33982682_12.jpg


The first one starts off easy but I found that it gets progress more challenging later on. So the rate of spread should be p'(t) which is:

p'(t) = 5/[e^.5t * (1+10e^(-.5t))^2]


As for 1b, I just used chain rule and product rule together to get:

f''(x) = 6xy'(x^2) + 4(x^3)g''(x^2)And finally, for the second question, if the tangent it horizontal, then dy/dx = 0, right?

Therefore, you solve for x, which leads you to:

sinx=-1
x=arcsin(-1)
x= -$\pi$/2


Which leads to ( -$\pi$/2 , 0 ) as the co-ordinates after substituting x = -$\pi$/2 into the original function.

Thanks in advance.
 
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I suspect you have posted the wrong image (containing the questions) here...
 
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