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Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a...

Let `f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040.` Then the value of `n` is________

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In (f(x))=In (x-1)+In (x-2)+...+In (x-n)
`"or "f'(x)=f(x)[(1)/(x-1)+(1)/(x-2)+...(1)/(x-n)]`
`=(x-2)(x-3)(x-n)+(x-1)(x-3)...(x-n)+...+(x-1)(x-2)...(x-(n-1))`
`"or "f'(n)=(n-1)(n-2)(n-3)cdot3.2cdot1`
(all other factors except the last vanishes when x=n)
`"or "5040=(n-1)!`
`"or "n=8`
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CENGAGE-DIFFERENTIATION-Exercise (Numerical)
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  4. If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(...

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  5. Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value ...

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  6. y=f(x) , where f satisfies the relation f(x+y)=2f(x)+x y(y)+ysqrt(f(x)...

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  7. If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime...

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  8. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

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  11. Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

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  12. A nonzero polynomial with real coefficients has the property that f(x)...

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  13. A function is reprersented parametrically by the equations x=(1+t)/(t^...

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  14. Let z=(cosx)hat5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=...

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  15. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

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  19. Let y be an implicit function of x defined by x^(2x)-2x^xcot y-1=0....

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