If `varphi(x)` is a polynomial function and `varphi^(prime)(x)>varphi(x)AAxgeq1a n dvarphi(1)=0,` then `varphi(x)geq0AAxgeq1` `varphi(x)

If varphi(x) is differentiable function AAx in R and a in R^+ such that varphi(0)=varphi(2a),varphi(a)=varphi(3a)a n dvarphi(0)!=varphi(a) then show that there is at least one root of equation varphi^(prime)(x+a)=varphi^(prime)(x)in(0,2a)

If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then (a) f^(prime)(a^+)=varphi(a) (b) f^(prime)(a^-)=-varphi(a) (c) f^(prime)(a^+)=f^(prime)(a^-) (d) none of these

The solution of the differential equation (dy)/(dx)=y/x+(varphi(y/x))/(varphi^(prime)(y/x)) is a. varphi(y/x)=k x b. x \ varphi\ (y/x)=k c. varphi\ (y/x)=k y d. y \ varphi(y/x)=k

Evaluate: int_(pi/4)^((3pi)/4) varphi/(1-sinvarphi)d varphi

If f(x)=|x-a|varphi(x) , where \ varphi(x) is continuous function, then f'(a^+)=varphi(a) (b) f^(prime)(a^-)=-varphi(a) (c) f^(prime)(a^+)=f'(a^-) (d) none of these

n{P(P(P(varphi)))}=

If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (a) (varphi^(prime)psi^('')-psi'varphi' ')/((varphi^(prime))^2) (b) (varphi^(prime)psi^('')-psi'varphi' ')/((varphi^(prime))^3) (c) varphi^('')/psi^('') (d) psi^('')/varphi^('')

If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (varphi^(prime)psi^-psi'varphi' ')/((varphi^(prime))^2) (b) (varphi^(prime)psi^-psi'varphi' ')/((varphi^(prime))^3) varphi^(/)psi^ (d) psi^(/)varphi^

If the function f(x) increases in the interval (a , b),a n dvarphi(x) [f(x)]^2 , then varphi(x) increases in (a , b) varphi(x) decreases in (a , b) we cannot say that varphi(x) increases or decreases in (a , b)dot none of these

If for the function varphi(x) = lambdax^2+7x-4 , varphi' (5) = 97, find lambda .