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)

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

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) (d) none of these

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

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