Let `f(x)=a x^2-b|x|,` where `aa n db` are constants. Then at `x=0,f(x)` has A. a maxima whenever `a >0,b >0` B. a maxima whenever `a >0,b<0` C. minima whenever `a >0,b<0` D. neither a maxima nor a minima whenever `a >0, b<0`

Let f(x) = a+ b|x| + c|x|^4 where a, b and continuous are real constants . Then, f(x) is differentiable at x = 0, if

Let f(x)={(absx, "for",0ltabsxlt=2),(1, "for",x=0):} Then ,at x = 0, f(x) has

Let f(x)=a x^2+b x+cdot Consider the following diagram. Then Fig c 0 a+b-c >0 a b c<0

Let f(x) = Ax^2+Bx+C where A,B,C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the number 2A, A+B and C are all integers. Conversely, prove that if the numbers 2A, A+B and C are all integer then f(x) is an integer whenever x is an integer.

Let h(x)=f(x)-(f(x))^2+(f(x))^3 for every real number xdot Then (a) h is increasing whenever f is increasing (b) h is increasing whenever f is decreasing (c) h is decreasing whenever f is decreasing (d) nothing can be said in general

If f(x)={{:(x^2,xlt=0) , (2sinx ,x >0):}' .Investigate the function at , x=0 for maxima/minima

Let f(x)=a x^2+bx +c a ,b ,c in R . If f(x) takes real values for real values of x and non-real values for non-real values of x , then (a) a=0 (b) b=0 (c) c=0 (d) nothing can be said about a ,b ,c .

Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5)=-3f(2) and that 3 is a root of f(x)=0. Then find the other root of f(x)=0.

If the line a x+b y+c=0 is a normal to the curve x y=1, then (a) a >0,b >0 (b) a >0,b >0 (d) a 0