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

If for the function "Phi"(x)=lambdax^2+7x-4,\ \ "Phiprime^"(5)=97 , find lambda .

If f(x)=lambdax^(2)+mux+12 , f'(4)=15 and f'(2)=11 , then find the value of lambda+mu .

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

Suppose, the function f(x)-f(2x) has the derivative 5 at x=1 and derivative 7 at x=2 . The derivative of the function f(x)-f(4x) at x=1 , has the value 10+lambda , then the value of lambda is equal to……..

Show that the function varphi defined by varphi(x)=cos x\ (x in RR) ; satisfies the initial value problem (d^2y)/(dx^2)+y=0, y(0)=1,\ y^(prime)(0)=0 .

Let alpha and beta be the values of x obtained form the equation lambda^(2) (x^(2)-x) + 2lambdax +3 =0 and if lambda_(1),lambda_(2) be the two values of lambda for which alpha and beta are connected by the relation alpha/beta + beta/alpha = 4/3 . then find the value of (lambda_(1)^(2))/(lambda_(2)) + (lambda_(2)^(2))/(lambda_(1)) and (lambda_(1)^(2))/lambda_(2)^(2) + (lambda_(2)^(2))/(lambda_(1)^(2))

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

The length of DNA a bacteriophage varphi 174 and lambda is

varphi ^2=0 represents

The values of lambda for which the function f(x)=lambdax^3-2lambdax^2+(lambda+1)x+3lambda is increasing through out number line (a) lambda in (-3,3) (b) lambda in (-3,0) (c) lambda in (0,3) (d) lambda in (1,3)