cheesecake
New member
- Joined
- Feb 28, 2021
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- 9
Can folks please help me with another question? Thanks
Draw a sketch of a curve y=e^(-2x) -3x . The curve crosses x-axis at A(a,0) and the y-axis at B(0,1). O is the origin
(a) write down an equation satisfied by a.
(b) Show that the tangent at A meets the y-axis at the point whose y-coordinate is 2ae^(-2a) +3a
(c) show that d2y/dx2>0 and using the results from parts(a) and b ,deduce that 6a^2+3a<1
(d) find ,in terms of a,the area of the region bounded by the curve and the line segments OA and OB
(e) By comparing this area with the area of the triangle OAB, show that 3a^2+4a>1 Hence show that (√7)/3 - 2/3 < a < (√33)/12 - 1/4
I have difficulty with c and e
Draw a sketch of a curve y=e^(-2x) -3x . The curve crosses x-axis at A(a,0) and the y-axis at B(0,1). O is the origin
(a) write down an equation satisfied by a.
(b) Show that the tangent at A meets the y-axis at the point whose y-coordinate is 2ae^(-2a) +3a
(c) show that d2y/dx2>0 and using the results from parts(a) and b ,deduce that 6a^2+3a<1
(d) find ,in terms of a,the area of the region bounded by the curve and the line segments OA and OB
(e) By comparing this area with the area of the triangle OAB, show that 3a^2+4a>1 Hence show that (√7)/3 - 2/3 < a < (√33)/12 - 1/4
I have difficulty with c and e