If equation `f(x)=x^4-a x^3+b x^2-c x+420` have all roots integer and greater than 1. Given that `f(4)=0,` then `f(-4)=0` (b) `f(8)=60` `f^(prime)(4)=3` (d) `f^(prime)(3)=-8`

If f(x)=|cosx| , find f^(prime)(pi/4) and f^(prime)((3pi)/4) .

If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0, then (a) f(4)=f(-4) (b) f(2)+f(-2)=0 (c) f^(prime)(4)+f^(prime)(-4)=0 (d) f^(prime)(2)=f^(prime)(-2)

If f^(prime)(x)=8x^3-2x ,f(2)=8, find f(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(x)=x^3+b x^2+c x+d and f(0),f(-1) are odd integers, prove that f(x)=0 cannot have all integral roots.

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 f^(prime)(c)=0 (b) f^(prime)(c)>0 f^(prime)(c)<0 (d) none of these

If is a real valued function defined by f(x)=x^2+4x+3, then find f^(prime)(1)a n df^(prime)(3)dot

Let y=f(x) be a parabola, having its axis parallel to the y-axis, which is touched by the line y=x at x=1. Then, (a) 2f(0)=1-f^(prime)(0) (b) f(0)+f^(prime)(0)+f^(0)=1 (c) f^(prime)(1)=1 (d) f^(prime)(0)=f^(prime)(1)

If f(x) =x^4-8x^3+4x^2+4x+39 and f (3 + 2i) = a + ib then a : b is equal to

If f(x)=(x+3)/(5x^2+x-1) and g(x)=(2x+3x^2)/(20+2x-x^2) such that f(x) and g(x) are differentiable functions in their domains, then which of the following is/are true (a) 2f^(prime)(2)+g^(prime)(1)=0 (b) 2f^(prime)(2)-g^(prime)(1)=0 (c) f^(prime)(1)+2g^(prime)(2)=0 (d) f^(prime)(1)-2g^(prime)(2)=0