Could you clarify the meaning of ‘the site of function of x’, for ‘a)’ ?
help pls
a) if d^2y/d^2x = 6x+4 and dy/dx=8 and y=2 when x=1, find your site a function of x
b) if f''(x)=x, f'(2)=1 and f (3)=0, find f (x)
c) if f''(x) =-2x and the curve y=f (x) has a stationary point at (2,6), find the equation of this curve
thank uu
Could you clarify the meaning of ‘the site of function of x’, for ‘a)’ ?
oh sorry - I meant "find y as a function of x"
For a)
d^2y/d^2x = 6x+4
dy/dx = 3x^2+4x+c1
Since dy/dx=8 when x=1
8 = 3(1)^2+4(1)+c1
c1 = -5
dy/dx = 3x^2+4x-5
y = x^3+2x^2-5x+c2
Since y=2 when x=1
2 = (1)^3+2(1)^2-5(1)+c2
c2 = 4
Therefore y = x^3+2x^2-5x+4
For b)
f''(x)=x
f'(x)=x^2/2+c1
Since f'(2)=1
1=(2)^2/2+c1
c1=-1
f'(x)=x^2/2-1
f(x)=x^3/6-x+c2
Since f(3)=0
0=(3)^3/6-(3)+c2
c2=-3/2
Therefore f(x)=x^3/6-x-3/2
Last edited by darkk_blu; 5 Feb 2018 at 9:18 PM.
thank you for the help!! <3
Generally with these types of questions you should write out the primitive function including any unknown constants, then use the points that are given to you to figure out what the constants are.
HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]
Also "has a stationary point at (2,6)" implies that at x=2, y'=0 and at x=2, y=6
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