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

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

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

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x=c . Then g^(prime)(f(x)) equal. (a) f^(prime)(c) (b) 1/(f^(prime)(c)) (c) f(c) (d) none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2 and y(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If f(x)=|cosx-sinx| , find f^(prime)(pi/6) and f^(prime)(pi/3) .

Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot Then inte^xf(x)dx is

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x) a tx=a is also the normal to y=f(x) a tx=b , then there exists at least one c in (a , b) such that (a)f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c)<0 (d) none of these

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real xdot Then g^('')(f(x)) equals. (a) -(f^('')(x))/((f^'(x))^3) (b) (f^(prime)(x)f^('')(x)-(f^(prime)(x))^3)/(f^(prime)(x)) (c) (f^(prime)(x)f^('')(x)-(f^(prime)(x))^2)/((f^(prime)(x))^2) (d) none of these