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1. Show that the function given by \(f\left(x\right)=\frac{log{x}}{x}\) has maximum at x=e.

3. Find the intervals in which the function f given by \(f\left(x\right)=\frac{4sin{x}-2x-xcos{x}}{2+cos{x}}\) is

(i) increasing

(ii) decreasing.

4. Find the intervals in which the function f given by \(f\left(x\right)=x^3+\frac{1}{x^3},x\neq0\) is

(i) increasing

(ii) decreasing.

10. Find the points at which the function f given by \(f(x)=(x–2)^4 (x+1)^3\) has

(i) local maxima

(ii) local minima

(iii) point of inflexion

16. A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of

(A) \(1 \ m^3/h\)

(B) \(0.1 \ m^3/h\)

(C) \(1.1 \ m^3/h\)

(D) \(0.5 \ m^3/h\)