SOLUTION: I'm Having hard time solving this homework. Can anyone help? 2. Calculate the points of the tangent of the curve : y = ex(x2 – 8) where and in which the tangent line is hor

Algebra ->  Trigonometry-basics -> SOLUTION: I'm Having hard time solving this homework. Can anyone help? 2. Calculate the points of the tangent of the curve : y = ex(x2 – 8) where and in which the tangent line is hor      Log On


   

Question 168096: I'm Having hard time solving this homework. Can anyone help?

2. Calculate the points of the tangent of the curve : y = ex(x2 – 8) where and in which the tangent line is horizontal

3. Write one of the two tangents to the curve : y = 1 + x³ which are parallel to this equation 12x - y = 1.

4. Calculate
I) If f(x) = ex cos x calculate f ’(x) et f ’’

(ii) Calculate (d99/ dx99) Sin x

5.
Calculate the derivative :
I) y = xe-x²

II) Let say: r(x) = f(g(h(x))) whit h(1) = 2, g(2) = 3, h’(1)= 4, g’(2) = 5, f’(3) = 6. Calculate r’(1).

III) Show that the function : y = Ae-x + Be-x satisfy the equation with differential y”+ 2y’+y = 0




Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
Hi here i answered questions 2) and 3) contact me if you need more help
2. Calculate the points of the tangent of the curve : y = ex(x2 – 8) where and in which the tangent line is horizontal
y=exp%28x%5E2-8%29 ,dy%2Fdx=2x%2Aexp%28x%5E2-8%29
y'=0 if only if x=0
then the point is (0,0) (where the tangent of the curve is horizontal)
3. Write one of the two tangents to the curve : y = 1 + x³ which are parallel to this equation 12x - y = 1.
12x-y=1
then
y+=+12x-1
y+=+1%2Bx%5E3 then dy%2Fdx=3x%5E2
then 12 (first term of 12x-1 and y'(x)= 3x^2 are the same}
12+=+3x%5E2 then x%5E2=4 then x=2 or x=-2
taking x=2 then equation of the line is y+=+%28dy%2Fdx%29%2A%282%29%28x-2%29%2By%282%29 where y%28x%29=1%2Bx%5E3
then line is y+=+12%28x-2%29%2B9=12x-15
Answer: y+=+12x-15