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 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 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)=x|x|, then prove that f^(prime)(x)=2|x|

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If f(x)=x|x|, then prove that f^(prime)(x)=2|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)<0 (d) none of these

If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,f(0)=3,f(pi/2)=5 . Find f(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)