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If f(x)=e^xg(2x),g(0)=4 and g'(0) = 2 th...

If `f(x)=e^xg(2x),g(0)=4` and g'(0) = 2 then f'(0) is equal to

A

4

B

6

C

8

D

12

Text Solution

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The correct Answer is:
C
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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. If x^2+y^2=t+1/t and x^4+y^4=t^2+1/t^2 then (dy)/(dx)=

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  2. If x=sin^(-1)(3t-4t^3),y=cos^(-1)(8t^4-8t^2+1) then (dy)/(dx)=

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  3. If f(x)=e^xg(2x),g(0)=4 and g'(0) = 2 then f'(0) is equal to

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  4. Let f(x)=sinx,g(x)=x^2 and h(x) = log x. If F(x)=(h(f(g(x)))), then F'...

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  5. If y = f(x) (dy)/dx=f'(x) therfore y=f{g(x)} then f'{g(x)} will be den...

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  6. If f(x)=xf(2a-x) then f''(0) equal to

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  7. If x=e^z then x^2(d^2y)/(dx^2) is

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  8. If S=t^3+6t^2-36t+100 . Determine acceleration and displacement at the...

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  9. x and y are the sides of two squares such that y=x-x^2 Find the rate o...

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  10. If f(x)=x/(sinx) and g(x)=x/("tan"x), where 0ltxle1, then in this inte...

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  11. The function f(x)=(sinx+cosx) is an increasing function in

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  12. If the function f(x)=2x^2-kx+5 is increasing on [1,2], then k lies in ...

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  13. Let f(x)=inte^x(x-1)(x-2)dx, then f(x) decreases in the interval

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  14. If f(x)={(3x^2+12x-1,-1lexle2),(37-x,2ltxle3):}

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  15. For all theta in [0,pi/2] show that cos(sintheta)gtsin(costheta)

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  16. Which of the following holds true for "x"in[0,pi/2)

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  17. The maximum value of ((logx)/x)is

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  18. The minimum value of (x^2+250/x) is

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  19. The minimum value of f(x)=3x^4-8x^3-48x+25 on [0.3] is

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  20. The maximum value of f(x)=(x-2)(x-3)^2 is

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